相关论文: Lawvere-Tierney sheaves, factorization systems, se…

We systematically investigate morphisms and equivalences of toposes from multiple points of view. We establish a dual adjunction between morphisms and comorphisms of sites, introduce the notion of weak morphism of toposes and characterize…

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages,…

Let $M$ be a closed manifold that admits a self-cover $p:M \to M$ of degree >1. We say p is strongly regular if all its iterates are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of $M$:…

Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…

Topological properties of the jacobian curve ${\mathcal J}_{\mathcal{F},\mathcal{G}}$ of two foliations $\mathcal{F}$ and $\mathcal{G}$ are described in terms of invariants associated to the foliations. The main result gives a decomposition…

Lie algebroids, singular foliations, and Dirac structures are closely related objects. We examine the relation between their pullbacks under maps satisfying a constant rank or transversality assumption. A special case is given by blowdown…

We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we…

To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…

Let M, N be monoids, and PSh(M), PSh(N) their respective categories of right actions on sets. In this paper, we systematically investigate correspondences between properties of geometric morphisms PSh(M) $\rightarrow$ PSh(N) and properties…

Let $\breve{K}$ be a complete discrete valuation field with an algebraically closed residue field ${k}$ and ring of integers $\breve{{O}}$. Let $T$ be a torus defined over $\breve{K}$. Let $L^+T$ denote the connected commutative…

We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map A_L: C->J, which maps C into its compactified Jacobian, and form…

We study several sufficient conditions for the molecularity/local-connectedness of geometric morphisms. In particuar, we show that if $\mathcal{S}$ is a Boolean topos then, for every hyperconnected essential geometric morphism ${p :…

We prove the compatibility of pushforward along a proper morphism of an \'{e}tale constructible sheaf and the pushforward of its characteristic cycle up to $p$-torsion. This was conjectured by Takeshi Saito. For this, we revisit the…

In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements. We also present a…

We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be…

We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category $\mathbb{EFF}$. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as…

The divisors on $\bar{\operatorname{M}}_g$ that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of $\operatorname{A}_g$ form a 2-dimensional extremal face of the nef cone of…

We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give…

We first prove semi-orthogonal decompositions of derived factorization categories arising from sums of potentials of gauged Landau-Ginzburg models, where the sums are not necessarily Thom--Sebastiani type. We then apply the result to the…

We develop a categorical framework for studying graphs of groups and their morphisms, with emphasis on pullbacks. More precisely, building on classical work by Serre and Bass, we give an explicit construction of the so-called…