Related papers: Canonical modules of complexes

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…

We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…

We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first…

In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.

We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…

Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…

We can define a module to be an exact functor on a small abelian category. This is explained and shown to be equivalent to the usual definition but it does offer a different perspective, inspired by the notions from model theory of…

In this paper we shall investigate the concepts of cofiniteness of local cohomology modules and Abelian categories of cofinite modules over arbitrary Noetherian rings. Then we shall improve some of the results given in the literature.

The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…

We consider endomorphism algebras of $n$-term silting complexes in derived categories of hereditary algebras, and we show that the module category of such an endomorphism algebra has a separated $n$-section. For $n=3$ we obtain a trisection…

The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…

Let $R$ be a polynomial ring over a field. We introduce the concept of sequentially almost Cohen-Macaulay modules and describe the extremal rays of the cone of local cohomology tables of finitely generated graded $R$-modules which are…

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We…

Let $R$ be a commutative noetherian ring, $\frak a$ be an ideal of $R$, $\mathcal{S}$ be an arbitrary Serre subcategory of $R$-modules satisfying the condition $C_{\frak a}$ and let $\mathcal{N}$ be the subcategory of finitely generated…

We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the…

We study properties of a map from a certain unitary group in $n$ variables to a related unitary group in $\binom{n}{k}$ variables. We explain how it gives rise to a map between canonical models of Shimura varieties and we prove that it…

We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra…

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.