Tootfinder

It doesn’t get as much play as the captain Picard “there are FOUR lights” scene, but I often think about this scene from “Babylon 5” about resisting “The system” and the question:
“But can you win?”
“Every time I say…no.”

Elliptic surfaces to class groups and Selmer groups
Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque
https://arxiv.org/abs/2509.00551 https://arxiv.org/pd…

Elliptic surfaces to class groups and Selmer groups
In this note, we connect the $n$-torsions of the Picard group of an elliptic surface to the $n$-divisibility of the class group of torsion fields for a given integer $n>1$. We also connect the $n$-divisibility of the Selmer group to that of the class group of torsion fields.

Localizing motives of Azumaya algebras
Maxime Ramzi
https://arxiv.org/abs/2509.01507 https://arxiv.org/pdf/2509.01507…

Localizing motives of Azumaya algebras
We prove that the natural map from the derived Brauer group of a qcqs scheme $X$ to the Picard group of $X$-linear motives is injective, extending results of Tabuada and Tabuada-Van den Bergh.

Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
Nicola Fabiano
https://arxiv.org/abs/2510.01496 https://arxiv.org/pdf…

Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
We introduce a novel class of self-mappings on metric spaces, called \textbf{PA-contractions} (Path-Averaged Contractions), defined by an averaging condition over iterated distances. We prove that every continuous PA-contraction on a complete metric space has a unique fixed point, and the Picard iterates converge to it. This condition strictly generalizes the classical Banach contraction principle. We provide examples showing that PA-contractions are independent of F-contractions, Kannan, Chatt…

from my link log —
Titan.DS: LCARS style Star Trek infographic.
https://www.mewho.com/titan/
saved 2025-10-30 https://dotat.at/:/NS1VJ.html

$K(1)$-local $K$-theory of Azumaya algebras
Maxime Ramzi
https://arxiv.org/abs/2509.01516 https://arxiv.org/pdf/2509.01516…

$K(1)$-local $K$-theory of Azumaya algebras
We study the decategorification process that takes an Azumaya algebra to its $K(1)$-local $K$-theory. We prove various injectivity statements and relate precisely certain Brauer groups (more precisely, spectra) to certain $K$-theoretic strict Picard spectra or strict unit spectra. For example, we prove that for fields $F$ of characteristic $\neq p$, $\mathbf{Br}(F)[p^{\infty}] \simeq \mathbb{G}_{\mathrm{pic}}(L_{K(1)}K(F)\otimes \mathbb{S}_{W(\overline{\mathbb F_p})})[p^\infty]$ where $\mathbb{…

Picard groups of quotient ring spectra
Ishan Levy, Guchuan Li, Ningchuan Zhang
https://arxiv.org/abs/2509.16695 https://arxiv.org/pdf/2509.16695

Picard groups of quotient ring spectra
We develop tools to study Picard groups of quotients of ring spectra by a finitely generated ideal, which we use to show that $\mathrm{Pic}(\mathrm{E}_n/I) = \mathbb{Z}/2$, where $\mathrm{E}_n$ is a Lubin--Tate theory and $I$ is an ideal generated by suitable powers of a regular sequence. We apply this to obtain spectral sequences computing Picard groups of $\mathrm{K}(n)$-local generalized Moore algebras, and make some preliminary computations including the height $1$ case.

Line bundles and exact sequences for the ideal class group and the Picard group
Abolfazl Tarizadeh
https://arxiv.org/abs/2508.19889 https://arxiv.org/pdf/2…

Line bundles and exact sequences for the ideal class group and the Picard group
For any extension of commutative rings $A\subseteq B$ we first naturally define a group $\Cl(A,B)$, that we call the ideal class group of this extension (we will see that both the classical ideal class group and, surprisingly, the Picard group are special cases of this structure), then, as a first main result, we obtain the following exact sequence of Abelian groups: ...

Tried to finally watch Star Trek: Picard and it’s so overwhelmingly awful that I literally couldn’t watch it.
I knew it had mixed review but holy shit. Like as in the actors couldn’t get themselves to act because the writing is so bad.

Towards the classification of Fano 4-folds with $b_2\geq 7$
C. Casagrande
https://arxiv.org/abs/2508.21207 https://arxiv.org/pdf/2508.21207

Towards the classification of Fano 4-folds with $b_2\geq 7$
We study (smooth, complex) Fano 4-folds X with Picard number rho(X)>6. We show that if rho(X)>9, then X is a product of del Pezzo surfaces, thus improving recent results by the author and by the author and S.A. Secci; the statement is now optimal. In the range rho(X)=7,8,9 we show that if X is not a product of surfaces, and has no small elementary contraction, then it is the blow-up of a cubic 4-fold along a special configuration of planes. When instead rho(X)>6 and X has a small elementary con…

Involutive Brauer groups and Poincar\'e rings
Viktor Burghardt, Noah Riggenbach, Lucy Yang
https://arxiv.org/abs/2509.25737 https://arxiv.org/pdf/2509.…

Involutive Brauer groups and Poincaré rings
We use the formalism of Poincaré $ \infty $-categories, as developed by Calmès-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus-Steimle, to define and study moduli stacks of line bundles with $ λ$-hermitian pairings and of Morita equivalence classes of Azumaya algebras equipped with an involution. Our moduli spaces give rise to enhancements of the ordinary Picard and Brauer groups which incorporate the data of an involution on the base; we will refer to these new invariants as the Poincaré …

Punk from The Voyage Home in Star Trek Picard (Kirk Thatcher cameo "I hate you" song)
https://www.youtube.com/watch?v=r6wDR6heQcU

Differential Equations for Wilson Loops in ABJM Theory
Takao Suyama
https://arxiv.org/abs/2509.16545 https://arxiv.org/pdf/2509.16545

Differential Equations for Wilson Loops in ABJM Theory
We derive a system of differential equations which are satisfied by the vevs of BPS Wilson loops and 't Hooft coupling of ABJM theory. They are Picard-Fuchs equations of an algebraic curve defined by the derivative of the planar resolvent of the corresponding matrix model. The weak and strong coupling behaviors can be reproduced by their local solutions around regular singularities. We also obtain a recursion relation which can be used to determine the planar vevs of BPS Wilson loops in arbitra…

An efficient splitting iteration for a CDA-accelerated solver for incompressible flow problems
Victoria L. Fisher, Leo G. Rebholz, Duygu Vargun
https://arxiv.org/abs/2509.12547 …

An efficient splitting iteration for a CDA-accelerated solver for incompressible flow problems
We propose, analyze, and test an efficient splitting iteration for solving the incompressible, steady Navier-Stokes equations in the setting where partial solution data is known. The (possibly noisy) solution data is incorporated into a Picard-type solver via continuous data assimilation (CDA). Efficiency is gained over the usual Picard iteration through an algebraic splitting of Yosida-type that produces easier linear solves, and accuracy/consistency is shown to be maintained through the use o…

My wife's not a SF person, but yesterday she had a far-reaching decision to make, so I persuaded her to watch Tapestry—the TNG episode where Q gives Picard the "It's a Wonderful Life" treatment. It made an impression! @… #StarTrek

Reactive Semantics for User Interface Description Languages
Basile Pesin (Federation ENAC ISAE-SUPAERO ONERA, Universite de Toulouse, France), Celia Picard (Federation ENAC ISAE-SUPAERO ONERA, Universite de Toulouse, France), Cyril Allignol (Federation ENAC ISAE-SUPAERO ONERA, Universite de Toulouse, France)
https://arxiv.org/abs/2508.1361…

Reactive Semantics for User Interface Description Languages
User Interface Description Languages (UIDLs) are high-level languages that facilitate the development of Human-Machine Interfaces, such as Graphical User Interface (GUI) applications. They usually provide first-class primitives to specify how the program reacts to an external event (user input, network message), and how data flows through the program. Although these domain-specific languages are now widely used to implement safety-critical GUIs, little work has been invested in their formalizat…

Je n'aurais jamais imaginé que la STM baptiserait une station de métro en honneur de Mary Two-Axe Earley.
Texte d'Isabelle Picard paru dans la Presse sur cette militante des droits des femmes des Premières Nations au Canada.
https://www.lapresse.ca/dialog…

Bienvenue à la station Mary-Two-Axe-Earley
La Société de transport de Montréal a dévoilé mardi matin le nom des futures stations du prolongement de la ligne bleue du métro de Montréal.

3D Human Pose and Shape Estimation from LiDAR Point Clouds: A Review
Salma Galaaoui, Eduardo Valle, David Picard, Nermin Samet
https://arxiv.org/abs/2509.12197 https://

3D Human Pose and Shape Estimation from LiDAR Point Clouds: A Review
In this paper, we present a comprehensive review of 3D human pose estimation and human mesh recovery from in-the-wild LiDAR point clouds. We compare existing approaches across several key dimensions, and propose a structured taxonomy to classify these methods. Following this taxonomy, we analyze each method's strengths, limitations, and design choices. In addition, (i) we perform a quantitative comparison of the three most widely used datasets, detailing their characteristics; (ii) we compile u…

On higher regulators of Picard modular surfaces
Linli Shi
https://arxiv.org/abs/2510.08708 https://arxiv.org/pdf/2510.08708

On higher regulators of Picard modular surfaces
We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in a paper of Loeffler\textendash Skinner\textendash Zerbes are in the motivic cohomology groups of the interior motives. Then we establish a relation between the motivic classes and non-critical values of the motivic $L$-functions associated to cuspidal automorphic representations of $\mathrm{GU}(2,1)$, thus deducing non-triviality of the motivic classes and provid…

Closing the Performance Gap in Generative Recommenders with Collaborative Tokenization and Efficient Modeling
Simon Lepage, Jeremie Mary, David Picard
https://arxiv.org/abs/2508.14910

Closing the Performance Gap in Generative Recommenders with Collaborative Tokenization and Efficient Modeling
Recent work has explored generative recommender systems as an alternative to traditional ID-based models, reframing item recommendation as a sequence generation task over discrete item tokens. While promising, such methods often underperform in practice compared to well-tuned ID-based baselines like SASRec. In this paper, we identify two key limitations holding back generative approaches: the lack of collaborative signal in item tokenization, and inefficiencies in the commonly used encoder-deco…

Autoequivalences of Fukaya categories of surfaces and graded gentle algebras
Sebastian Opper
https://arxiv.org/abs/2510.11543 https://arxiv.org/pdf/2510.11…

Autoequivalences of Fukaya categories of surfaces and graded gentle algebras
We compute the derived Picard groups of partially wrapped Fukaya categories of surfaces in the sense of Haiden-Katzarkov-Kontsevich and the related graded gentle algebras. An important ingredient in characteristic zero is the exponential map from Hochschild cohomology to the derived Picard group introduced in recent work by the author. To prove our results in positive characteristic, we combine deformation theory and formality results for Hochschild complexes. Along the way we show that the sur…

Trivializing Torsors for Difference Algebraic Groups
Annette Bachmayr, Michael Wibmer
https://arxiv.org/abs/2509.22095 https://arxiv.org/pdf/2509.22095

Trivializing Torsors for Difference Algebraic Groups
We study torsors for groups defined by algebraic difference equations. Our main result provides necessary and sufficient conditions on the base difference field for all such torsors to be trivial. We also present an application to the uniqueness of difference Picard-Vessiot extensions for linear differential equations.

A classification algorithm for reflexive simplices
Marco Ghirlanda
https://arxiv.org/abs/2510.09131 https://arxiv.org/pdf/2510.09131

A classification algorithm for reflexive simplices
We present a general classification algorithm for reflexive simplices, which allows us to determine all reflexive simplices in dimensions five and six. In terms of algebraic geometry this means that we classify the Gorenstein fake weighted projective spaces in dimensions five and six. As a byproduct of our methods, we obtain explicit formulae for the Picard group and the Gorenstein index of any fake weighted projective space.

Learning Mean-Field Games through Mean-Field Actor-Critic Flow
Mo Zhou, Haosheng Zhou, Ruimeng Hu
https://arxiv.org/abs/2510.12180 https://arxiv.org/pdf/25…

Learning Mean-Field Games through Mean-Field Actor-Critic Flow
We propose the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), combining techniques from reinforcement learning and optimal transport. The MFAC framework jointly evolves the control (actor), value function (critic), and distribution components through coupled gradient-based updates governed by partial differential equations (PDEs). A central innovation is the Optimal Transport Geodesic Picard (OTGP) flow, which drives the distributio…

Suppression of the induced gravitational wave background due to third-order perturbations
Raphael Picard, Luis E. Padilla, Karim A. Malik, David J. Mulryne
https://arxiv.org/abs/2509.07811

Suppression of the induced gravitational wave background due to third-order perturbations
In this work, we revisit and evaluate new source terms which contribute to the induced gravitational wave background. We study their respective contributions to the stochastic gravitational wave background by computing their spectral densities in a radiation-dominated universe. These terms appear at third order in cosmological perturbation theory, however, their correlations with primordial gravitational waves are non-trivial and appear at the same order as so-called scalar induced and scalar-t…

The Motivic Picard--Lefschetz Formula
Ran Azouri, Emil Jacobsen
https://arxiv.org/abs/2510.12762 https://arxiv.org/pdf/2510.12762

The Motivic Picard--Lefschetz Formula
We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an embedding of projective hypersurfaces.

A three-dimensional acousto-optic deflector
Lewis R. B. Picard, Manuel Endres
https://arxiv.org/abs/2510.07633 https://arxiv.org/pdf/2510.07633

A three-dimensional acousto-optic deflector
Acousto-optic deflectors (AODs) are widely used across physics, microscopy, neuroscience, and laser engineering, providing fast, precise, and non-mechanical control of light. While conventional AODs naturally support multiplexing in one and two dimensions, no analogous device has existed for three-dimensional control, leaving a critical gap in rapid focus tuning and 3D beam shaping. Here we demonstrate a three-dimensional AOD system capable of multiplexed axial and lateral beam control with hig…

Crosslisted article(s) found for physics.app-ph. https://arxiv.org/list/physics.app-ph/new
[1/1]:
- A three-dimensional acousto-optic deflector
Lewis R. B. Picard, Manuel Endres

Tame nodal stacky curves
Martin Bishop, William C. Newman
https://arxiv.org/abs/2509.20629 https://arxiv.org/pdf/2509.20629

Tame nodal stacky curves
In this paper we analyze the properties of tame nodal stacky curves, in particular twisted curves and \textit{doubly-twisted} curves. Our main results are a complete classification of the possible structures of a tame stacky node, along with computations of the Picard and Brauer groups of nodal stacky curves.

Crosslisted article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- On higher regulators of Picard modular surfaces
Linli Shi
https://

Picard group action on the category of twisted sheaves
Ting Gong, Yeqin Liu, Yu Shen
https://arxiv.org/abs/2508.09379 https://arxiv.org/pdf/2508.09379

Picard group action on the category of twisted sheaves
In this paper, we study the category of twisted sheaves over a scheme $X$. Let $\mathcal{M}$ be a quasi-coherent sheaf on $X$, and $α$ in $\operatorname{Br}(X)$. We show that the functor $ - \otimes_{\mathcal{O}_X} \mathcal{M} : \operatorname{QCoh}(X, α) \to \operatorname{QCoh}(X, α) $ is naturally isomorphic to the identity functor if and only if $\mathcal{M}\cong \mathcal{O}_{X}$. As a corollary, the action of $\operatorname{Pic}(X)$ on $D^{b}(X, α)$ is faithful for any Noetherian scheme …

WESLEY: ‘Then she actually complimented Captain Picard on his legs?’
DATA: ‘I would have thought a telepath would be more discreet, sir.’
RIKER: ‘Exactly the opposite. She knows what’s on your mind, and she lets you know what’s on hers.’
#StarTrek #TNG 2x19

Crosslisted article(s) found for math.KT. https://arxiv.org/list/math.KT/new
[1/1]:
- On higher regulators of Picard modular surfaces
Linli Shi
https://

Higher direct images of dualizing sheaves III
J\'anos Koll\'ar, S\'andor J. Kov\'acs
https://arxiv.org/abs/2508.16507 https://arxiv.org/pdf…

Higher direct images of dualizing sheaves III
We show that for flat morphisms between varieties with rational singularities, the higher direct images of the structure sheaf are locally free. As a consequence, the identity component of the relative Picard scheme is a smooth algebraic group scheme.

The Euler characteristic of an endotrivial complex
Nadia Mazza, Sam K. Miller
https://arxiv.org/abs/2508.07404 https://arxiv.org/pdf/2508.07404

The Euler characteristic of an endotrivial complex
Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We examine the Lefschetz homomorphism $Λ: \mathcal{E}_k(G) \to O(T(kG))$ from the group of endotrivial complexes, i.e. the Picard group of the bounded homotopy category of $p$-permutation modules $K^b({}_{kG}\mathbf{triv})$, to the orthogonal unit group of the Grothendieck group of $K^b({}_{kG}\mathbf{triv})$, i.e. the trivial source ring. When $p = 2$ and $k = \mathbb{F}_2$, $Λ$ is surjective when $G$ has a Sylow $2$-subg…

Classification of del {P}ezzo surfaces of rank one. III. Height 3
Karol Palka, Tomasz Pe{\l}ka
https://arxiv.org/abs/2508.13609 https://arxiv.org/pdf/2508.…

Classification of del {P}ezzo surfaces of rank one. III. Height 3
This article is a part of a series aimed at classifying normal del Pezzo surfaces of Picard rank one over an algebraically closed field of arbitrary characteristic, up to an isomorphism. The key invariant guiding our classification is the height, defined as the minimal number $h$ such that the minimal resolution of singularities admits a $\mathbb{P}^1$-fibration whose fiber meets the exceptional divisor $h$ times. It is expected that every singular del Pezzo surface of rank one is of height $h\…

On the Direct Problem in Differential Galois Theory for the Classical Groups
Daniel Robertz, Matthias Seiss
https://arxiv.org/abs/2510.07323 https://arxiv.…

On the Direct Problem in Differential Galois Theory for the Classical Groups
Let $G$ be a classical group of Lie rank $l$ and let $C$ be an algebraically closed field of characteristic zero. For $l$ differential indeterminates $\boldsymbol{v}=(v_1,\dots,v_l)$ over $C$ we constructed in a previous paper a general Picard-Vessiot extension $\mathcal{E}$ of the differential field $C\langle \boldsymbol{s}(\boldsymbol{v})\rangle$ having differential Galois group $G(C)$. Here $ \boldsymbol{s}(\boldsymbol{v})=(s_1(\boldsymbol{v}),\dots,s_l(\boldsymbol{v}))$ are certain differen…

Symmetric power of higher dimensional varieties
Ashima Bansal, Supravat Sarkar, Shivam Vats
https://arxiv.org/abs/2508.12654 https://arxiv.org/pdf/2508.126…

Symmetric power of higher dimensional varieties
We study several properties of the symmetric power $S^mX$ of a smooth variety $X$. We describe the Picard and divisor class groups of $S^mX$ when $X$ is projective. We give a complete description of the stratification of $S^mX$ by iterated singular locus in terms of some combinatorial data regarding partitions of the integer $m.$ This gives a new viewpoint of a natural stratification of $S^mX$ by multiplicities.

Abel maps for integral curves via a derived perspective
Qingyuan Jiang
https://arxiv.org/abs/2508.11786 https://arxiv.org/pdf/2508.11786

Abel maps for integral curves via a derived perspective
We develop a general framework for Abel maps associated with a family $X/S$ of integral curves using derived algebraic geometry. For compactified Picard schemes, our approach yields relative quasi-smooth derived enhancements of the Quot schemes $\mathrm{Quot}_{ω/X/S}^d$ and, in the Gorenstein case, of the Hilbert schemes of points $\mathrm{Hilb}_{X/S}^d$ on $X/S$. These constructions naturally generalize to higher rank torsion-free sheaves and their coherent systems. We obtain unified semior…

Nef cones of Hilbert schemes of points on some K3 surfaces
Uttaran Dutta, Sean Edwards, Neelarnab Raha
https://arxiv.org/abs/2509.10724 https://arxiv.org/p…

Nef cones of Hilbert schemes of points on some K3 surfaces
Let $X$ be a Mori dream K3 surface of Picard rank $2$. We compute the nef cone of the Hilbert scheme $X^{[n]}$ of $n$ points on $X$ for large $n$ using Bridgeland stability methods. We also find bounds on the nef cone for small $n$. Studying the geometry of a $2$-to-$1$ cover $X\rightarrow Q$ of a smooth quadric $Q$ in $\mathbb{P}^3$, and its induced rational map $X^{[2]}\dashrightarrow Q^{[2]}$ on the Hilbert schemes, we calculate the nef cone of $X^{[2]}$ in a particular case. Finally, we als…

Logarithmic Geometry and Geometric Class Field Theory
Aaron Slipper
https://arxiv.org/abs/2508.08648 https://arxiv.org/pdf/2508.08648

Logarithmic Geometry and Geometric Class Field Theory
In this paper, we provide an upgrade of Deligne's geometric class field theory for tamely ramified Galois groups using logarithmic geometry. In particular, we define a framed logarithmic Picard space, and show that a logarithmic compactification of the classical tamely ramified Div-to-Pic map has, for sufficiently large degree, log simply connected fibers given by loagrithmically compactified vector spaces. This provides a canonical bijection between local systems on the curve with divisorial l…

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- On higher regulators of Picard modular surfaces
Linli Shi
https://

Dual of Algebraic Geometry codes from Hirzebruch surfaces
Alix Barraud
https://arxiv.org/abs/2509.07761 https://arxiv.org/pdf/2509.07761

Dual of Algebraic Geometry codes from Hirzebruch surfaces
In this paper, we give an explicit form for the dual of the algebraic geometry code $C_e(a,b)$ defined on an Hirzebruch surface $\mathcal{H}_e$ and parametrized by the divisor $aS_e + bF_e$, where $a,b\in\mathbb{N}$ and $S_e$ and $F_e$ generate the Picard group $\mathrm{Pic}( \mathcal{H}_e)$. Notably, we compute a lower bound for the minimum distance of $C_e(a,b)^\perp$. One of the main ingredient for our study is a new explicit form of the code $C_e(a,b)$ which we provide at the beginning of t…