Tootfinder

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.

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…

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.

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…

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…

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, …

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…

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.

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/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…

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.

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.

This https://arxiv.org/abs/2305.03876 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The nil-Brauer category
We introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies the split iquantum group of rank one. As this iquantum group is a basic building block for $\imath$-quantum groups of higher rank, we expect that the nil-Brauer category will play a role in future developments related to the categorification of quantum symmetric pairs.

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}.

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.

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…

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.

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.

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.

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 …

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…