Related papers: Freyd's generating hypothesis for groups with peri…

For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor,…

Cohomology of Specht modules for the symmetric group can be equated in low degrees with corresponding cohomology for the Borel subgroup B of the general linear group GL_d(k), but this has never been exploited to prove new symmetric group…

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

Let $k$ be a commutative Noetherian ring and $\underline{\mathscr{C}}$ be a locally finite $k$-linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion…

We prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2-multiplicative. We also give an explicit construction of the transgression map…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

Let $\mathfrak F$ be a locally compact nonarchimedean field with residue characteristic $p$ and $G$ the group of $\mathfrak{F}$-rational points of a connected split reductive group over $\mathfrak{F}$. We define a torsion pair in the…

Let G be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k fusion ring R_k(G) of G with the twisted equivariant K-homology at level k+h, where h is the dual Coxeter number. In this…

We study the question of the existence of a Waldhausen category on any (relative) abelian category in which the contractible objects are the (relatively) projective objects. The associated $K$-theory groups are "stable algebraic…

We study the cohomology of Aut(F_n) and Out(F_n) with coefficients in the modules \wedge^q H, \wedge H^*, Sym^q H or Sym^q H^*, where H is the Out(F_n)-module obtained by abelianising the free group F_n. For reasons which are not…

In this work we construct a compactly generated tensor-triangulated stable category for a large class of infinite groups, including those in Kropholler's hierarchy $\mathrm{LH}\mathfrak{F}$. This can be constructed as the homotopy category…

Let $G$ be a finite soluble group and $G^{(k)}$ the $k$th term of the derived series of $G$. We prove that $G^{(k)}$ is nilpotent if and only if $|ab|=|a||b|$ for any $\delta_k$-values $a,b\in G$ of coprime orders. In the course of the…

Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse decomposition. When…

We examine the cohomology and representation theory of a family of finite supergroup schemes of the form $(\mathbb G_a^-\times \mathbb G_a^-)\rtimes (\mathbb G_{a(r)}\times (\mathbb Z/p)^s)$. In particular, we show that a certain relation…

We prove some conditions for higher dimensional algebraic fibering of pro-$p$ group extensions and we establish corollaries about incoherence of pro-$p$ groups. In particular, if $G = K \rtimes \Gamma$ is a pro-$p$ group, $\Gamma$ a…

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local…

Let $\mathfrak F$ be a formation and let $G$ be a group. A subgroup $H$ of $G$ is $\mathrm{K}\mathfrak F$-subnormal (submodular) in $G$ if there is a subgroup chain $H=H_0\le \ H_1 \le \ \ldots \le H_i \leq H_{i+1}\le \ldots \le \ H_n=G$…

We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series -…

In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear supergroup. Some of these classes restrict to the universal…

Let F be a field, let G be its absolute Galois group, and let R(G, k) be the representation ring of G over a suitable field k. In this preprint we construct a ring homomorphism from the mod 2 Milnor K-theory k_*(F) to the graded ring gr…