Related papers: Decompositions of the stable module $\infty$-categ…

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

We consider an arbitrary topological group $G$ definable in a structure $\mathcal M$, such that some basis for the topology of $G$ consists of sets definable in $\mathcal M$. To each such group $G$ we associate a compact $G$-space of…

Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p > 0$. This paper continues a long-standing effort to classify the connected reductive subgroups of $G$. Having previously…

In this paper we develop a theory of stability for $G$-categories (presheaf of categories on the orbit category of $G$), where $G$ is a finite group. We give a description of Mackey functors as $G$-commutative monoids exploit it to…

Let G be a totally disconnected, locally compact group. A closed subgroup of G is locally normal if its normaliser is open in G. We begin an investigation of the structure of the family of closed locally normal subgroups of G. Modulo…

The theory of support varieties gives a rich supply of examples of thick subcategories of the stable module category of a finite group algebra. We study direct sum decompositions of such categories. We give examples where there are finer…

Given a finite group $G$ and a commutative ring $G$-spectrum $R$, we study the separable commutative algebras in the category of compact $R$-modules. We isolate three conditions on the geometric fixed points of $R$ which ensure that every…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

We prove that the only separable commutative ring-objects in the stable module category of a finite cyclic p-group G are the ones corresponding to subgroups of G. We also describe the tensor-closure of the Kelly radical of the module…

A persistence module is a functor $f: \mathbf{I} \to \mathsf{E}$, where $\mathbf{I}$ is the poset category of a totally ordered set. This work introduces saecular decomposition: a categorically natural method to decompose $f$ into simple…

This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors $\Def ^{\h}(E)$,…

We show that a pointwise finite-dimensional persistence module indexed over a small category decomposes into a direct sum of indecomposables with local endomorphism rings. As an application of this result we give new, short proofs of…

We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

We study the higher derived functors of the inverse limit of a functor F: D --> Z_{(p)}-mod, where D is one of the standard categories which arise when studying the homotopy theory of the classifying space of a finite group G, e.g., the…

While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not…

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the…

Let $kG$ be the group algebra of a finite group scheme defined over a field $k$ of characteristic $p>0$. Associated to any closed subset $V$ of the projectivized prime ideal spectrum $\operatorname{Proj} \operatorname{H}^*(G,k)$ is a thick…

We apply poset cocalculus, a functor calculus framework for functors out of a poset, to study the problem of decomposing multipersistence modules into simpler components. We both prove new results in this topic and offer a new perspective…

We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. We show the existence of a recollement of the above quotient category and it has the…