Tootfinder

Universal Characteristic-free Resolution of Singularities, I
Yi Hu
https://arxiv.org/abs/2507.21400 https://arxiv.org/pdf/2507.21400

Universal Characteristic-free Resolution of Singularities, I
We prove that for any singular integral affine variety $X$ of finite presentation over a perfect field defined over $\mathbb Z$, there exists a smooth morphism from $Y$ onto $X$ such that $Y$ admits a resolution. That is, there exists a smooth scheme $\widetilde{Y}$ and a projective birational morphism from $\widetilde{Y}$ onto $Y$, followed by a smooth morphism from $Y$ onto $X$. Our approach differs fundamentally from existing methods, as we neither restrict to any specific singular variety…

Morphisms and comorphisms of sites II - Distributors of sites
Axel Osmond, Olivia Caramello
https://arxiv.org/abs/2507.20932 https://arxiv.org/pdf/2507.209…

Morphisms and comorphisms of sites II - Distributors of sites
We introduce a notion of distributor of sites, involving suited analogs of flatness and cover-preservation, and show that this notion jointly generalizes those of morphism and comorphism of sites. Given two sites, we exhibit an adjunction between the category of distributors of sites between them and the category of geometric morphisms between the associated sheaf topoi; this adjunction restricts to an equivalence between geometric morphisms and continuous distributors of sites. We finally disc…

Rank one summands of Frobenius pushforwards of line bundles on G/P
Feliks R\k{a}czka
https://arxiv.org/abs/2507.20759 https://arxiv.org/pdf/2507.20759

Rank one summands of Frobenius pushforwards of line bundles on G/P
Let $X=G/P$ be a partial flag variety, where $G$ is a semi-simple, simply connected algebraic group defined over an algebraically closed field $K$ of positive characteristic. Let $\mathsf{F}\colon X\to X$ be the absolute Frobenius morphism. Given a line bundle $\mathscr{L}$ on $X$ and an integer $r\geq1$, we describe all line bundles that are direct summands of the pushforward $\mathsf{F}_{*}^{r}\mathscr{L}$. For $\mathscr{L}$ corresponding to a dominant weight, we also compute, for $r$ suffici…

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Jakob Ulmer
https://arxiv.org/abs/2507.15445 https://

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invari…

Minimal value set binomials and Frobenius nonclassical curves
Tiago Aprigio, Jo\~ao Paulo Guardieiro
https://arxiv.org/abs/2508.16541 https://arxiv.org/pdf…

Minimal value set binomials and Frobenius nonclassical curves
In this paper, we characterize all minimal value set binomials over $\mathbb{F}_q$, that is, binomials whose size of the set of images is the smallest possible. With this information, we also classify all quadrinomial curves with separated variables that are $\mathbb{F}_q$-Frobenius nonclassical for the morphism of lines.

Recursive characterisation of skew morphisms of finite cyclic groups
Martin Bachrat\'y, Michal Hagara
https://arxiv.org/abs/2506.11626 https://

Recursive characterisation of skew morphisms of finite cyclic groups
A skew morphism of a finite group $G$ is an element $φ$ of $\mathrm{Sym}(G)$ preserving the identity element of $G$ and having the property that for each $a\in G$ there exists a non-negative integer $i_a$ such that $φ(ab)=φ(a)φ^{i_a}(b)$ for all $b\in G$. In this paper we show that if a skew morphism $φ$ of $\mathbb{Z}_n$ is not an automorphism of $\mathbb{Z}_n$, then it is uniquely determined by a triple $(h,α,β)$ where $h$ is an element of $\mathbb{Z}_n$, $α$ is a skew morphism of $\m…

This https://arxiv.org/abs/2405.12717 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups
We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E_8. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E_7-bundle over the four-dimensional sphere. We use the results to detect nontrivial elements in the kernel of the reduced Thom morphism for Lie groups and their clas…

Category $\mathcal{O}$ and asymptotic characters
Alexis Leroux-Lapierre
https://arxiv.org/abs/2507.16215 https://arxiv.org/pdf/2507.1…

Category $\mathcal{O}$ and asymptotic characters
This paper defines an asymptotic character map which is a morphism from the Grothendieck group of category $\mathcal{O}$ of an integral filtered quantization to rational functions on the Lie algebra of a torus. We show that the asymptotic character of a module computes the equivariant multiplicity of its characteristic cycle. We then apply this construction to truncated shifted Yangians coming from simple, simply-laced Lie algebras and draw connections with characters of modules over KLR algebr…

Regular homomorphisms, with a twist
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
https://arxiv.org/abs/2506.17033 https://ar…

Regular homomorphisms, with a twist
Let $X/K$ be a variety over a field, and $A/K$ an abelian variety. A regular homomorphism to $A$ (in codimension $i$) induces, for every smooth geometrically connected pointed $K$-scheme $(T,t_0)$ and every cycle class $Z \in CH^i(T\times X)$, a morphism $T \to A$ of varieties over $K$. In this note we show that, if $T$ admits no $K$-point, the data $(T,Z)$ determines a torsor $A^{(T,Z)}$ over $K$ under $A$ and a $K$-morphism $T \to A^{(T,Z)}$. This can be used to provide an obstruction to the …

The odd spectral localiser via asymptotic morphisms and quasi-projections
Yuezhao Li, Bram Mesland
https://arxiv.org/abs/2506.17143 https://

The odd spectral localiser via asymptotic morphisms and quasi-projections
We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spectral truncation. We achieve this by pairing the K-theory class with an asymptotic morphism determined by the unbounded Kasparov module. We interpret the spectral localiser of Loring and Schulz-Baldes as an instance of such an index pairing.

Words avoiding the morphic images of most of their factors
Pascal Ochem, Matthieu Rosenfeld
https://arxiv.org/abs/2506.13368 https://…

Words avoiding the morphic images of most of their factors
We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$, distinct from the identity, such that $w$ contains $m(f)$. We show that every infinite binary word contains an imaged factor of length at least 6 and that 6 is best possible. We show that every infinite binary word contains at least 36 distinct imaged factors and that 36 is best possible.

Local fibrations and morphisms of relative toposes
L\'eo Bartoli, Olivia Caramello
https://arxiv.org/abs/2507.14379 https://arxiv…

Local fibrations and morphisms of relative toposes
We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to this more general setting. As an application of this notion, we obtain a characterization of the functors between relative sites that induce a morphism between the corresponding relative toposes: these are exactly the morphisms of sites which are morphisms of lo…

A categorical formulation of the Deligne-Terasoma approach to double shuffle theory
Benjamin Enriquez, Khalef Yaddaden
https://arxiv.org/abs/2506.15348 htt…

A categorical formulation of the Deligne-Terasoma approach to double shuffle theory
In this paper, we introduce the notion of a bimodule with a factorization structure (BFS) and show that such a structure gives rise to an algebra morphism. We then prove that this framework offers an interpretation of the geometric construction underlying both the Betti and de Rham harmonic coproducts of the double shuffle theory developed in \cite{DeT, EF1, EF2, EF3}.

C*-submodule preserving module mappings on Hilbert C*-modules
Michael Frank
https://arxiv.org/abs/2507.11206 https://arxiv.org/pdf/25…

C*-submodule preserving module mappings on Hilbert C*-modules
Let $A$ be a (non-unital, in general) C*-algebra with center $Z(M(A))$ of its multiplier algebra, and let $X$ be a full Hilbert $A$-module. Then any injective bounded module morphism $T$, for which every norm-closed $A$-submodule of $X$ is invariant, is of the form $T=c \cdot {\rm id}_X$ where $c \in Z(M(A))$. The same is true if the restriction to be norm-closed is dropped. At the other extrem, for two given strongly Morita equivalent C*-algebras $A$ and $B$ and an $A$-$B$ equivalence bimodule…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Cofinal morphism of polynomial monads and double delooping
Florian De Leger
h…

Generalized Symmetries From Fusion Actions
Chongying Dong, Siu-Hung Ng, Li Ren, Feng Xu
https://arxiv.org/abs/2508.13063 https://arxiv.org/pdf/2508.13063…

Generalized Symmetries From Fusion Actions
Let $A$ be a condensable algebra in a modular tensor category $\EuScript{C}$. We define an action of the fusion category $\EuScript{C}_A$ of $A$-modules in $\EuScript{C}$ on the morphism space $\mbox{Hom}_{\EuScript{C}}(x,A)$ for any $x$ in $\EuScript{C}$, whose characters are generalized Frobenius-Schur indicators. This fusion action can be considered on $A$, and we prove a categorical generalization of Schur-Weyl duality for this action. For any fusion subcategory $\EuScript{B}$ of $\EuScript…

Note on the linearisation of finite abelian groups
Aur\'elien Djament (CNRS, LAGA)
https://arxiv.org/abs/2507.13047 https://arxiv…

Note on the linearisation of finite abelian groups
If $K$ is a field \textit{with enough roots of unity} and $V$ an abelian group, the $K$-algebra $K[V]$ of the group $V$ is split semisimple, so that the canonical morphism $K[V]\to K^{V^\sharp}$, where $V^\sharp$ denotes the dual group of $V$ (which may be seen as Hom$(V,K^\times)$), is an isomorphism of $K$-algebras. If one removes the assumption that $K$ has enough roots of unity, one can easily deduce from it (by using a base change and Krull-Schmidt) that it remains a $K$-linear isomorphism…

Intersection of two quadrics: modular interpretation and Hitchin morphism
Vladimiro Benedetti, Andreas H\"oring, Jie Liu
https://arxiv.org/abs/2506.04707

Intersection of two quadrics: modular interpretation and Hitchin morphism
The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a structure of moduli space of twisted Spin-bundles. This generalises the classical result for threefolds, in which case it recovers the Hitchin fibration for the moduli space of rank two bundles with fixed determinant of odd degree on a curve of genus two.

On the compatibility of the Betti harmonic coproduct with cyclotomic filtrations
Benjamin Enriquez, Khalef Yaddaden
https://arxiv.org/abs/2508.12208 https://

On the compatibility of the Betti harmonic coproduct with cyclotomic filtrations
In a previous paper, the second author introduced a Betti counterpart of $N$-cyclotomic double shuffle theory for any $N \geq 1$. The construction is based on the group algebra of the free group $F_2$, endowed with a filtration relative to a morphism $F_2 \to μ_N$ (where $μ_N$ is the group of $N$-th roots of unity). One of the main results therein is the construction of a complete Hopf algebra coproduct $\widehatΔ^{\mathcal{W}, \mathrm{B}}_N$ on the relative completion of a specific subalgeb…

This https://arxiv.org/abs/2501.04357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generators of top cohomology
Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f : \mathrm{H}^n(X, ω_{X/R}) \to R$ is an isomorphism when $f$ has geometrically connected fibres. We construct an exact sequence that generates $\mathrm{Ext}_X^n(\mathcal{O}_X, ω_{X/R}) = \mathrm{H}^n(X, ω_{X/R})$ as an $R$-module in the following cases: (1) when $R$ is…

Tropical Donagi theorem
Felix R\"ohrle (Eberhard Karls Universit\"at T\"ubingen), Thomas Saillez (Universit\'e Libre de Bruxelles)
https://arxiv.org/abs/2507.05987

Tropical Donagi theorem
The tropical $n$-gonal construction was introduced in recent work by the first author and D.~Zakharov and structural results for $n = 2,3$ were established. In this article we explore the construction for $n = 4$ and prove a tropical analogue of Donagi's theorem which states that the tetragonal construction is a triality which preserves Prym varieties. This confirms the speculations in previous work and establishes new results on the non-injectivity of the tropical Prym-Torelli morphism. Finall…

Rooted tree modules
Suraj Mishra, Amit Kuber
https://arxiv.org/abs/2508.07435 https://arxiv.org/pdf/2508.07435

Rooted tree modules
A rooted tree module (RTM) $M:=M(T,F)$ over a zero-relation algebra $Λ:=\mathcal KQ/\langleρ\rangle$ over a field $\mathcal K$ is given by the data of a quiver morphism $F:T\to Q$ from a rooted tree $T$ (either with a source or a sink) taking paths in $T$ to paths in $Q$ not lying in $\langleρ\rangle$. When $\mathrm{char}(\mathcal K)\neq2$, we provide a checkable combinatorial characterization of the indecomposability of the RTM $M$ in terms of non-existence of idempotent quiver morphisms $�…

Universally Equidimensional Morphisms and Weakly or Strongly rational Singularities
Mohamed Kaddar
https://arxiv.org/abs/2507.03345 https://

Universally Equidimensional Morphisms and Weakly or Strongly rational Singularities
The focus of this article is the study of a certain type of singularities and their transfer properties in a universally equidimensional morphism (i.e. an open morphism with constant pure-dimensional fibers). The singularities of interest are those called weakly rational, characterized by the vanishing of the (m-1)-th direct image of the structural sheaf in a given desingularization of a complex space of dimension $m$. If the singular locus of the considered space has codimension at least two, …

Kummers, spinors, and heights
Jef Laga, Jack A. Thorne
https://arxiv.org/abs/2507.06865 https://arxiv.org/pdf/2507.06865

Kummers, spinors, and heights
Let $f(x) = x^{2g+1} + c_1 x^{2g} + \dots + c_{2g+1} \in k[x]$ be a polynomial of nonzero discriminant, and let $J$ denote the Jacobian of the odd hyperelliptic curve $C : y^2 = f(x)$. We show that the morphism $J \to \mathbb{P}^{2^g-1}$ associated to the linear system $|2 Θ|$ may be described explicitly, for any $g \geq 1$, using the theory of pure spinors. We apply this theory to study the heights of rational points in $J(k)$, when $k$ is a number field. As a particular consequen…

Comparison of Cohomological and K-theoretical Hall algebra
Felix K\"ung, \v{S}pela \v{S}penko
https://arxiv.org/abs/2507.08417 https://

Comparison of Cohomological and K-theoretical Hall algebra
We give a more conceptual construction of a comparison algebra morphism from the K-theoretical Hall algebra to a twist of the cohomological Hall algebra associated to a symmetric quiver, and extend the result to quivers with potential.

A motivic discrepancy function on arc spaces
Tommaso de Fernex, Zach Mere
https://arxiv.org/abs/2508.12420 https://arxiv.org/pdf/2508.12420

A motivic discrepancy function on arc spaces
At the heart of motivic integration is a change-of-variables formula which relates motivic integrals along proper birational maps of varieties. The formula was first proved by Kontsevich for smooth blow-ups of smooth varieties, and extended to arbitrary resolutions of singularities by Denef and Loeser. The purpose of this paper is to establish a general change-of-variables formula for a proper birational morphism of arbitrary varieties in arbitrary characteristics that does not rely on resoluti…

Baues-Wirsching Cohomology and Svarc Genus in Small Categories
Isaac Carcac\'ia-Campos, Enrique Mac\'ias-Virg\'os, David Mosquera-Lois
https://arxiv.org/abs/2508.00727

Baues-Wirsching Cohomology and Svarc Genus in Small Categories
We prove that for a bifibration P between small categories, the lenght of the cup product in the kernel of the induced morphism in the Baues-Wirsching cohomology with coefficients in any natural system is a lower bound for the homotopic sectional category (also called Svarc genus). Our results extend classical Svarc type inequalties to the categorical setting and introduce a computationally efficient method via a reduced cochain complex for Baues-Wirching cohomology.

A cohomological smoothness conjecture for moduli of mixed characteristic local shtukas with one leg
Sean Howe
https://arxiv.org/abs/2508.11595 https://arxi…

A cohomological smoothness conjecture for moduli of mixed characteristic local shtukas with one leg
We give a simple geometric characterization of the locus where the inscribed Banach--Colmez Tangent Spaces of moduli of mixed characteristic local shtukas with one leg and fixed determinant are connected. We conjecture that the structure morphism for the underlying diamond is cohomologically smooth over this locus and, applying the Fargues--Scholze Jacobian criterion, we prove this conjecture in the case of EL infinite level Rapoport--Zink spaces, generalizing a result of Ivanov--Weinstein in t…

On the vanishing of Ext and Tor
Abdolnaser Bahlekeh, Shokrollah Salarian
https://arxiv.org/abs/2507.05825 https://arxiv.org/pdf/2507.…

On the vanishing of Ext and Tor
This paper contains two theorems concerning the vanishing of natural transformations of (co)homology functors. Precisely, assume that $R$ is a right noetherian ring and $f: M\rt N$ is a morphism of finitely generated right $R$-modules. The first theorem proves that the natural transformation $\Ext^1(f, -)$ vanishes over the category of finitely generated right $R$-modules if and only if $\Tor_1(f, -)$ vanishes over the category of finitely generated left $R$-modules. As a corollary of this resu…

Coherent configurations and Frobenius structures
Gejza Jen\v{c}a, Anna Jen\v{c}ov\'a, Dominik Lachman
https://arxiv.org/abs/2507.21774 https://arxiv.or…

Coherent configurations and Frobenius structures
We prove that coherent configurations can be represented as modules over Frobenius structures in the category of real nonnegative matrices. We generalize the notion of admissible morphism from association schemes to coherent configurations. We show that the Frobenius structure associated to a coherent configuration can be modified to become a dagger Frobenius structure, and use this to connect the coherent configurations to groupoids and $H^*$-algebras. We examine the properties of the dagger F…

Frobenius liftable hypersurfaces
Tatsuro Kawakami, Supravat Sarkar, Jakub Witaszek
https://arxiv.org/abs/2507.12198 https://arxiv.org…

Frobenius liftable hypersurfaces
Let $D$ be a reduced divisor in $\mathbb P^n_k$ for an algebraically closed field $k$ of positive characteristic $p > 0$. We prove that if $(\mathbb P^n_k, D)$ is Frobenius liftable modulo $p^2$, then $D$ is a toric divisor. As a corollary, we show that if there exists a finite surjective morphism $f\colon Y\to X$ onto a smooth projective complex variety $X$ of Picard rank $1$ such that $(Y, f^{-1}(D)_{\mathrm{red}})$ is a toric pair, then $X$ is the projective space and $D$ is a toric divisor.

Lefschetz morphisms on singular cohomology and local cohomological dimension of toric varieties
Hyunsuk Kim, Sridhar Venkatesh
https://arxiv.org/abs/2506.03026

Lefschetz morphisms on singular cohomology and local cohomological dimension of toric varieties
Given a proper toric variety and a line bundle on it, we describe the morphism on singular cohomology given by the cup product with the Chern class of that line bundle in terms of the data of the associated fan. Using that, we relate the local cohomological dimension of an affine toric variety with the Lefschetz morphism on the singular cohomology of a projective toric variety of one dimension lower. As a corollary, we show that the local cohomological defect is not a combinatorial invariant. W…

Surjectivity and flatness over DVR's (after Moret-Bailly)
Benedictus Margaux
https://arxiv.org/abs/2506.01313 https://arxiv.org/p…

Surjectivity and flatness over DVR's (after Moret-Bailly)
We study morphisms of schemes $f : X \to S$ which are locally of finite type. We present conditions under which there exists a morphism $g : S'\to X$ of $S$--schemes such that $f \circ g $ is the canonical morphism $S'\to S$. Furthermore, we exhibit situations in which $f$ is flat surjective. Our results are mostly concerned with $S$ being the spectrum of a DVR.

When is the diagonal contractible?
Xi Chen, Frank Gounelas
https://arxiv.org/abs/2507.21889 https://arxiv.org/pdf/2507.21889…

When is the diagonal contractible?
For a smooth projective complex variety $X$, we prove that there exists a birational morphism $X\times X\to Y$ to a projective variety $Y$ contracting the diagonal $Δ_X\subset X\times X$ to a point if and only if $X$ has maximal Albanese dimension and irregularity $q\geq 2\dim X$. We also give necessary and sufficient conditions for arbitrary contractions of the diagonal and for the existence of a birational morphism which is an isomorphism outside the diagonal.

(BAA)-branes from higher Teichm\"uller theory
Eric Y. Chen, Enya Hsiao, Mengxue Yang
https://arxiv.org/abs/2508.09562 https://arxiv.org/pdf/2508.09562…

(BAA)-branes from higher Teichmüller theory
Interpreting certain holomorphic Lagrangians that arise from the relative Langlands program, we construct moduli stacks underlying the generalized Slodowy categories of Collier--Sanders and $G^\mathbf{R}$-Higgs bundles over a Riemann surface. Furthermore, we extend the Cayley correspondence of Bradlow--Collier--García-Prada--Gothen--Oliveira to a morphism of Lagrangians over the Hitchin moduli stack, and initiate the study of its hyperholomorphic mirror partner under $S$-duality.

Trace for the Du Bois complex
Hyunsuk Kim
https://arxiv.org/abs/2507.07350 https://arxiv.org/pdf/2507.07350

Trace for the Du Bois complex
We construct some version of the trace morphism between the Du Bois complexes, with applications towards the behavior of the local cohomological dimension and some Hodge theoretic aspects of singularities under finite morphisms.

This https://arxiv.org/abs/2309.14542 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Trace Maps on Rigid Stein Spaces
We provide a relative version of the trace map from the work of Beyer, which can be associated to any finite tale morphism $X \to Y$ of smooth rigid Stein spaces and which then relates the Serre duality on $X$ with the Serre duality on $Y$. Furthermore, we consider the behaviour of any rigid Stein space under (completed) base change to any complete extension field and deduce a commutative diagram relating Serre duality over the base field with the Serre duality over the extension field.

Varieties with representable CH_0-group and a question of Colliot-Th\'{e}l\`{e}ne
Claire Voisin
https://arxiv.org/abs/2508.02331 https://arxiv.org/pdf/…

Varieties with representable CH_0-group and a question of Colliot-Thélène
We continue our investigation of the geometry of the Albanese morphism on 0-cycles. We provide an example of a smooth projective variety with representable CH_0-group but with no universal 0-cycle, which answers a question asked by Colliot-Thélène. Our construction relies on a counterexample to the integral Hodge conjecture provided by Benoist and Ottem.

Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Yohsuke Matsuzawa
https://arxiv.org/abs/2507.05027

Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Consider a dominant rational self-map $f$ on a smooth projective variety $X$ defined over $\overline{\mathbb{Q}}$. We prove that \begin{align} \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x)) } = 0, \end{align} where $h_{Y}$ is a height associated with a closed subscheme $Y \subset X$ of codimension $c$, $h_{H}$ is any ample height on $X$, and $x \in X(\overline{\mathbb{Q}})$ is a point with well-defined orbit, under the following assumptions: (1) either $f$ is a morphism, or $Y$ is p…

This https://arxiv.org/abs/1509.07195 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Clifford algebra of a finite morphism
We develop a general theory of Clifford algebras for finite morphisms of schemes and describe applications to the theory of Ulrich bundles and connections to period-index problems for curves of genus 1.

Isomorphism of \'etale fundamental groups lifts to isomorphism of stratified fundamental group
Indranil Biswas, Manish Kumar, A. J. Parameswaran
https://arxiv.org/abs/2506.03829

Isomorphism of étale fundamental groups lifts to isomorphism of stratified fundamental group
It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the étale fundamental groups, then the induced map of the stratified fundamental groups $π_1^{str}(f)\, :\, π_1^{str}(Y,\, y)\,\longrightarrow\, π_1^{str}(X,\, f(y))$ is also an isomorphism.

Quasi-canonical lifting of projective varieties in positive characteristic
Ryo Ishizuka, Kazuma Shimomoto
https://arxiv.org/abs/2506.01345 https://

Quasi-canonical lifting of projective varieties in positive characteristic
The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by showing a descending property of such Frobenius liftability. We establish a refined form of the classical result due to Mehta-Srinivas on the existence of canonical liftings. For this purpose, we also establish a result on the algebraization of certain $p$-ad…

Holomorphic 1-forms without zeros on K\"ahler threefolds
Simon Pietig
https://arxiv.org/abs/2506.22067 https://arxiv.org/pdf/250…

Holomorphic 1-forms without zeros on Kähler threefolds
We classify all smooth compact connected Kähler threefolds that admit the structure of a $C^\infty$-fiber bundle over the circle. This generalizes the work of Hao and Schreieder in the projective case. In contrast to the projective case, there cannot always exist a smooth morphism to a positive-dimensional torus. Instead, we show that such a compact Kähler threefold admits a finite étale cover that is bimeromorphic to a $\mathbb{P}^1$-, $\mathbb{P}^2$-, or Hirzebruch surface-bundle over a lo…