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

A stable $\infty$-category is $1$-semiadditive if the norms for all finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of $1$-semiadditivity…

We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.

The purpose of this paper is to initiate a new attack on Arveson's resistant conjecture, that all graded submodules of the $d$-shift Hilbert module $H^2$ are essentially normal. We introduce the stable division property for modules (and…

We give a decomposition as a direct sum of indecomposable modules of several types of Specht modules in characteristic $2$. These include the Specht modules labelled by hooks, whose decomposability was considered by Murphy. Since the main…

We establish a decomposition of stable homology of automorphism groups of free groups with polynomial contravariant coefficients in term of functor homology. This allows several explicit computations, intersecting results obtained by…

We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…

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…

In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…

Homotopy type theory is a logical setting based on Martin-L\"of type theory in which geometric constructions and proofs can be carried out synthetically. Here, types can be interpreted as spaces up to homotopy, and proofs as…

Let $A$ be a cocommutative finite dimensional Hopf algebra over the field with two elements, satisfying some mild hypothesis. We set up a descent spectral sequence which computes the Picard group of the stable category of modules over $A$.…

We study the ring of differential operators D(X) on the basic affine space X=G/U of a complex semisimple group G with maximal unipotent subgroup U. One of the main results shows that the cohomology group H^*(X,O_X) decomposes as a finite…

Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…

Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The…

Let S=Sym(\Omega) be the group of all permutations of a countably infinite set \Omega, and for subgroups G_1, G_2\leq S let us write G_1\approx G_2 if there exists a finite set U\subseteq S such that < G_1\cup U > = < G_2\cup U >. It is…

We give concrete DG-descriptions of certain stable categories of maximal Cohen-Macaulay modules. This makes in possible to describe the latter as generalized cluster categories in certain cases.

Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner, the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterized in…

We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli…

The moduli space $\cM_g$ of nonsingular projective curves of genus $g$ is compactified into the moduli $\bcM_g$ of Deligne-Mumford stable curves of genus $g$. We compactify in a similar way the moduli space of abelian varieties by adding…

In this paper, we prove that the naive deformation problem of an $\mathbb{E}_n$-monoidal stable $k$-linear $\infty$-category $\mathcal{C}$ is a $2$-proximate formal $\mathbb{E}_{n+2}$-moduli problem, whose corresponding formal moduli…

We study Swan modules, which are a special class of projective modules over integral group rings, and their consequences for the homotopy classification of CW-complexes. We show that there exists a non-free stably free Swan module, thus…