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...

Let A L $A_L$ be the right-angled Artin group associated with a finite flag complex $L$ . We show that amenable category of equals virtual cohomological dimension Coxeter W $W_L$ In particular, groups satisfy question Capovilla–Löh–Moraschini proposing an inequality between and Farber's topological complexity.

Let R be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules (M, N) over R we study applications of rigidity of Tor(M, N), based on ideas by Huneke, Wiegand and Jorgensen. We then focus on the hypersurfaces with isolated singularity and even dimension, and show that modules over such rings behave very much like those over regular local rings. Connecti...

We establish a Grothendieck–Lefschetz theorem for smooth ample subvarieties of projective varieties over an algebraically closed field characteristic zero and, more generally, whose complement has small cohomological dimension. A weaker statement is also proved in general context and all characteristics. Several applications are included.

Methods are developed to relate the action of a principal fibration relative Whitehead products in order determine homotopy type certain spaces. The methods applied thoroughly analyze based loops on cell attachments. Key examples (n-1)-connected Poincare Duality complexes dimension 2n or 2n+1 with minor cohomological conditions.