Related papers: Abelian Groups in omega-categories

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…

In this paper we prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes. The characterization is given among a…

This work originates from chapters V and VII of Grothendieck's manuscript Pursuing Stacks, which contains a series of questions, as well as a previously unexplored formalism, concerning the interactions between the notion of test categories…

Let us consider an abelian variety defined over $\mathbb{Q_{\ell}}$ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the $\ell$-torsion points of the…

We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…

Derived decompositions of abelian categories are introduced in internal terms of abelian subcategories to construct semi-orthogonal decompositions (or Bousfield localizations, or hereditary torsion pairs) in various derived categories of…

It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantity which depends on the genus of the base curve and on bad…

By the algebraization of affine Nash groups, a connected affine Nash group is an abelian Nash manifold if and only if its algebraization is a real abelian variety. We first classify real abelian varieties up to isomorphisms. Then with a bit…

We explore the notion of representation of an affine extension of an abelian variety -- such an extension is a faithfully flat affine morphism of $\Bbbk$-group schemes $q:G\to A$, where $A$ is an abelian variety. We characterize the…

Let $X$ be a smooth complex algebraic variety and let $\operatorname{Coh} (X)$ denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the deformation theory of $\operatorname{Coh}…

We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan…

Semi-abelian and finitely cocomplete homological categories are characterized in terms of four resp. three simple axioms, in terms of the basic categorical notions introduced in the first few chapters of MacLane's classical book. As an…

A countable semigroup is $\aleph_0$-categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into the $\aleph_0$-categoricity of semigroups. Our main results are a…

In this article, we study the cuts of a totally ordered abelian group $\Gamma$. We begin by recalling some results on ordered sets I and on the associated sets IS(I) and FS(I) of initial and final segments of I. For a totally ordered set I…

For a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a…

Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of…

We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also calculate the group of exact…

We identify a class of "quasi-compact semi-separated" (qcss) twisted presheaves of algebras A for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch(A) are defined. This class is stable under algebraic…

We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian varieties. We also give a generalization to higher genera of the famous formula $12…

We define admissible and weakly admissible subcategories in exact categories and prove that the former induce semi-orthogonal decompositions on the derived categories. We develop the theory of thin exact categories, an exact-category…