We prove that every amenable group of cohomological dimension two whose integral ring is a domain solvable and investigate certain homological finiteness properties groups satisfy the analytic zero divisor conjecture act on an acyclic CW-complex with stabilisers.

Abstract We study the Hodge filtration on local cohomology sheaves of a smooth complex algebraic variety along closed subscheme Z in terms log resolutions and derive applications regarding cohomological dimension, Du Bois complex, vanishing reflexive differentials associated to .

This article is part of the program studying large-scale geometric properties totally disconnected locally compact groups, TDLC-groups, by analogy with theory for discrete groups. We provide a characterization hyperbolic in terms homological isoperimetric inequalities. used to prove main result article: TDLC-groups rational cohomological dimension $\leq 2$, hyperbolicity inherited compactly pre...

We prove a power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL2 over any number field that is not totally real. Our proof involves the theory of p-adically completed cohomology developed by Calegari and Emerton and a bound for the growth of coinvariants in certain finitely generated noncommutative Iwasawa modules.

The mapping class group of a topological space is the group of self-homeomorphisms modulo the equivalence relation of isotopy. For 2-manifolds (of finite type), it is a discrete group which is known (see [M, HI, H2, H3, H4]) to share many of the properties of arithmetic subgroups of linear algebraic groups, although it is not arithmetic. In this note we describe the results of [Ml], which show ...

Abstract We consider finite-dimensional Hopf algebras $u$ that admit a smooth deformation $U\to u$ by Noetherian algebra $U$ of finite global dimension. Examples such include small quantum groups over the complex numbers, restricted enveloping in characteristic, and Drinfeld doubles height $1$ group schemes. provide means analyzing (cohomological) support for representations $u$, via singularit...