Related papers: Some stable non-elementary classes of modules

To each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category Aff(C)_\kappa of smooth modules (in the sense of Kazhdan and…

Let $(R,\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\ge}-1$ be an integer and $ r=\depth_k(I,N)$ the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M.…

Let $p \geq 5$ be a prime number and let $G = SL_2(\mathbb{Q}_p)$. Let $\Xi$ = Spec$(Z)$ denote the spectrum of the centre $Z$ of the pro-$p$ Iwahori Hecke algebra of $G$ with coefficients in a field $k$ of characteristic $p$. Let…

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…

Let $\tilde{G}$ be a finite group, $G$ a normal subgroup of $\tilde{G}$ and $k$ an algebraically closed field of characteristic $p>0$. The first main result in this paper is to show that support $\tau$-tilting $k\tilde{G}$-modules…

Motivated by bifurcation of branches of homoclinic orbits of dynamical systems, we consider families of first-order equations on the real line and introduce a generalisation of previous index theorems by Pejsachowicz, and by Hu and…

We show that the Kazhdan-Lusztig category $KL_k$ of level-$k$ finite-length modules with highest-weight composition factors for the affine Lie superalgebra $\widehat{\mathfrak{gl}(1|1)}$ has vertex algebraic braided tensor supercategory…

We describe the modules in the Ziegler closure of ray and coray tubes in module categories over finite-dimensional algebras. We improve slightly on Krause's result for stable tubes by showing that the inverse limit along a coray in a ray or…

It is well-known that a class of all modules, which are torsion-free with respect to a set of ideals, is closed under injective envelopes. In this paper, we consider a kind of a dual to this statement - are the divisibility classes closed…

We prove an analogue of the Gabriel--Quillen embedding theorem for exact $\infty$-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact $\infty$-category. Moreover, we construct a symmetric monoidal…

Let $C$ be a polarized nodal curve of compact type. In this paper we study coherent systems $(E,V)$ on $C$ given by a depth one sheaf $E$ having rank $r$ on each irreducible component of $C$ and a subspace $V \subset H^0(E)$ of dimension…

Deligne's category $\underline{{\rm Rep}}(S_t)$ is a tensor category depending on a parameter $t$ "interpolating" the categories of representations of the symmetric groups $S_n$. We construct a family of categories $\mathcal{C}_\lambda$…

We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only…

A famous theorem of Nakaoka asserts that the cohomology of the symmetric group stabilizes. The first author generalized this theorem to non-trivial coefficient systems, in the form of $\mathrm{FI}$-modules over a field, though one now…

Solid modules over $\mathbb{Q}$ or $\mathbb{F}_p$, introduced by Clausen and Scholze, are a well-behaved variant of complete topological vector spaces that forms a symmetric monoidal Grothendieck abelian category. For a discrete field $k$,…

We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this setting both K-theory and THH carry universal properties, the…

We initiate the study of profinite rigidity for modules over a Noetherian domain: to what extent are these objects determined by their finite images? We establish foundational statements in analogy to classical results in the category of…

Combining results from Keller and Buchweitz, we describe the 1-periodic derived category of a finite dimensional algebra $A$ of finite global dimension as the stable category of maximal Cohen-Macaulay modules over some Gorenstein algebra…

Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then…