相关论文: On the degree-wise coherence of FI_G-modules

Given a non-negative integer $n$ and a ring $R$ with identity, we construct an abelian model structure on the category of left $R$-modules where the class of cofibrant objects coincides with $\mathcal{GF}_n(R)$ the class of left $R$-modules…

Let $G$ be a simple simply connected algebraic group over an algebraically closed field $k$ of characteristic $p$, with $r$-th Frobenius kernel $G_r$. Let $M$ be a $G_r$-module and $V$ a rational $G$-module. We put a variety structure on…

We resolve a conjecture of Li and Ramos that relates the regularity of an FI-module to its local cohomology groups. This is an analogue of the familiar relationship between regularity and local cohomology in commutative algebra.

We show that an abelian category can be exactly, fully faithfully embedded into a module category as the right perpendicular subcategory to a set of modules or module morphisms if and only if it is a locally presentable abelian category…

We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

Let R be a commutative Noetherian domain, and let M and N be finitely generated R-modules. We give new criteria for determining when M tensor N has torsion. We also give constructive formulas for producing a module in the isomorphism class…

We present a new method for combining two cotorsion pairs to obtain an abelian model structure and we apply it to construct and study a new model structure on left $R$-modules over a left coherent ring $R$. Its class of fibrant objects is…

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, $\mathcal{PGF}$, (respectively that of projectively coresolved Gorenstein $\mathcal{B}$ flat modules,…

We investigate infinite dimensional modules for a linear algebraic group $\mathbb G$ over a field of positive characteristic $p$. For any subcoalgebra $C \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we consider…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $\widehat{R}$ its $\mathfrak{m}$-adic completion. We study the problem of determining when a finitely generated $\widehat{R}$-module arises from an $R$-module, i.e., when it is…

We establish an inequality relating the projective dimension of a DG-module in $\mathrm{D}^\mathrm{b}_\mathrm{f}(A)$ to its grade and introduce the concept of perfect DG-modules as a natural generalization of perfect modules. It is proved…

The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…

In this paper we improve recent results dealing with cellular covers of $R$-modules. Cellular covers (sometimes called co-localizations) come up in the context of homotopical localization of topological spaces. They are related to…

In this note, we survey two instances in the representation theory of finite-dimensional algebras where the quantity of a type of structures is intimately related to the size of those same structures. More explicitly, we review the fact…

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1…

Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated. Let H be…

We prove a general structure theorem for finitely presented torsion modules over a class of commutative rings that need not be Noetherian. As a first application, we then use this result to study the Weil- \'etale cohomology groups of…

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.