Related papers: Comparison of Abelian categories recollements

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…

ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).

If A and B are abelian varieties over a number field K such that there are non-trivial geometric homomorphisms of abelian varieties between reductions of A and B at most primes of K, then there exists a non-trivial (geometric) homomorphism…

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…

In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…

In this short note, we show a p-adic analogue of Beilinson's equivalence comparing two derived categories: the derived category of holonomic modules and derived category of modules whose cohomologies are holonomic.

Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…

Two concepts of being Archimedean are defined for arbitrary categories.

Let $E$ be an elliptic curve over a field $k$. Let $R:= \text{End}\, E$. There is a functor $\mathscr{H}\!\!\mathit{om}_R(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties…

For abelian length categories the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length…

We introduce $n$-abelian and $n$-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that $n$-cluster-tilting subcategories of abelian (resp. exact) categories…

We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.

We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same for…

We prove a connexity theorem for abelian varieties in characteristic $0$: if $X$ is an abelian variety and $V\rightarrow X$ and $W\rightarrow X$ two morphisms, then, under certain hypotheses, the fiber product of $V$ and $W$ over $X$ is…

Let $A \leq G$ be a subgroup of a group $G$. An $A$-complement of $G$ is a subgroup $H$ of $G$ such that $G = A H$ and $A \cap H = \{1\}$. The \emph{classifying complements problem} asks for the description and classification of all…

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…

We give a presentation of abelian class field theory.

Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…

We classify all $2$-blocks with abelian defect groups of rank $4$ up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application…

We describe an linear representation for Abel-Grassmann groups. As a consequence, we obtain or improve many previous results. In particular, enumeration of Abel-Grassmann groups up to isomorphism is obtained for orders <512.