Related papers: Brauer's height zero conjecture for quasi-simple g…

Using a stable equivalence due to Rouquier, we prove that Broue's abelian defect group conjecture holds for 3-blocks of defect 2 whose Brauer correspondent has a unique isomorphism class of simple modules. The proof makes use of the fact,…

We relate the n! conjecture (by Garsia and Haiman) to the geometry of principal nilpotent pairs, and state a conjecture generalizing the n! conjecture to arbitrary semisimple algebraic groups. We also show, using Borel's fixed point…

We prove that if all the simple groups involved in a finite group $G$ satisfy the `inductive Feit condition', then Walter Feit's conjecture from 1980 holds for $G$. In particular, this would solve Brauer's Problem 41 from 1963 in the…

The purpose of this article is to prove that Gersten's conjecture for a commutative regular local ring is true. As its applications, we will prove the vanishing conjecture for certain Chow groups, generator conjecture for certain $K$-groups…

The first author has recently classified the Morita equivalence classes of 2-blocks B of finite groups with elementary abelian defect group of order 32. In all but three cases he proved that the Morita equivalence class determines the…

We give formulas for calculating the unramified Brauer group of a homogeneous space $X$ of a semisimple simply connected group $G$ with finite geometric stabilizer $\bar F$ over a wide family of fields of characteristic 0. When $k$ is a…

We provide new conditions for the Strong Atiyah conjecture to lift to finite group extensions. In particular, we show cocompact special groups satisfy these conditions, so the Strong Atiyah conjecture holds for virtually cocompact special…

This paper is a contribution to the general program introduced by Isaacs, Malle and Navarro to prove the McKay conjecture in the representation theory of finite groups. We develop new methods for dealing with simple groups of Lie type in…

We study a group which is hyperbolic relative to a finite family of infinite subgroups. We show that the group satisfies the coarse Baum-Connes conjecture if each subgroup belonging to the family satisfies the coarse Baum-Connes conjecture…

We present a generalization of Brouwer's conjectural family of inequalities -- a popular family of inequalities in spectral graph theory bounding the partial sum of the Laplacian eigenvalues of graphs -- for the case of abstract simplicial…

The Equidistribution Conjecture is proved for general semiabelian varieties over number fields. Previously, this conjecture was only known in the special case of almost split semiabelian varieties through work of Chambert-Loir. The general…

Let $\mathcal X$ be a regular variety, flat and proper over a complete regular curve over a finite field, such that the generic fiber $X$ is smooth and geometrically connected. We prove that the Brauer group of $\mathcal X$ is finite if and…

In this paper we develop techniques for computing the relative Brauer group of curves, focusing particularly on the case where the genus is 1. We use these techniques to show that the relative Brauer group may be infinite (for certain…

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…

A torsor under a k-group scheme G on a variety X over a number field k imposes a descent obstruction against the existence of rational points on X. We discuss the finite descent obstruction, that is for all such torsors under finite…

A condition is given, under which a general lattice point counting function is asymptotic to the corresponding ball volume growth function. This is then used to give height asymptotics in the style of the Batyrev-Manin Conjecture for…

This article is the final one of a series of articles on certain blocks of modular representations of finite groups of Lie type and the associated geometry. We prove the conjecture of Brou\'e on derived equivalences induced by the complex…

A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional $\sk$-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of…

Slattery has generalized Brauer's theory of p-blocks of finite groups to pi-blocks of pi-separable groups where pi is a set of primes. In this setting we show that the order of a defect group of a pi-block B is bounded in terms of the…