Related papers: Zassenhaus filtrations as intersections

We describe the perverse filtration in cohomology using the Lefschetz Hyperplane Theorem.

We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the…

We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for…

We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the…

Let $\H_n$ be a (degenerate or non-degenerate) Hecke algebra of type $G(\ell,1,n)$, defined over a commutative ring $R$ with one, and let $S(\bmu)$ be a Specht module for $\H_n$. This paper shows that the induced Specht module…

To a finitely generated profinite group $G$, a formal Dirichlet series $P_G(s)=\sum_{n \in \mathbb N} {a_n(G)}/{n^s}$ is associated, where $a_n(G)=\sum_{|G:H|=n}\mu(H, G)$ and $\mu(H,G)$ denotes the M\"obius function of the lattice of open…

A translation surface in the Heisenberg group is constructed as the product of two planar curves. We classify a type of such surfaces with vanishing intrinsic curvature by analyzing the determinant of their Gauss map

One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial…

We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…

We generalise to profinite groups some of our previous results on the cohomology of pro-p groups of bounded sectional p-rank.

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…

We find surface subgroups in certain one-relator groups with torsion and use this to deduce a profinite criterion for a word in the free group to be primitive.

We study the kernels of representations of mapping class groups of surfaces on twisted homologies of configuration spaces. We relate them with the kernel of a natural twisted intersection pairing: if the latter kernel is trivial then the…

We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.

We exploit the classical correspondence between finitely generated abelian groups and abelian complex algebraic reductive groups to study the intersection theory of translated subgroups in an abelian complex algebraic reductive group, with…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the…

The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…

Steinberg pro-groups are certain pro-groups used to analyze ordinary Steinberg groups locally in Zariski topology. In this paper we show that Steinberg pro-groups associated with general linear groups, odd unitary groups, and Chevalley…