Related papers: A proof of the Baum-Connes conjecture for reductiv…

Let $F$ be a finite group. We consider the lamplighter group $L=F\wr\mathbb{Z}$ over $F$. We prove that $L$ has a classifying space for proper actions $\underline{E} L$ which is a complex of dimension two. We use this to give an explicit…

Brou\'{e}'s Abelian Defect Conjecture predicts interesting derived equivalences between derived categories of modular representations of finite groups. We investigate a generalization of Brou\'{e}'s Conjecture to ring spectrum coefficients…

The generalized Effros-Hahn conjecture for groupoid C*-algebras says that, if G is amenable, then every primitive ideal of the groupoid C*-algebra C*(G) is induced from a stability group. We prove that the conjecture is valid for all second…

Let $G$ be a locally compact group, and let $B(G)$ denote its Fourier--Stieltjes algebra. We show that $B(G)$ is Connes-amenable if and only if $G$ is almost abelian.

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant…

Let $A$ be a regular ring of dimension $\le 2$. Let $G$ be a reductive group over $A$ such that its derived group is a split, i.e. a Chevalley--Demazure, semisimple group. We prove that every Zariski-locally trivial principal $G$-bundle…

It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is…

Let $G$ be a connected reductive group scheme acting on a spherical scheme $X$. In the case where $G$ is of type $A_n$, Aizenbud and Avni proved the existence of a number $C$ such that the multiplicity $\dim\hom(\rho,\mathbb{C}[X(F)])$ is…

We show that the statement analogous to the Mumford-Tate conjecture for abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associated Hodge group and the unipotent part of the image…

Bourbaki seminar 1062, October 2012.

We show that the classical Baum-Connes assembly map is quantitatively an isomorphism for a class of lacunary hyperbolic groups, and we explain how to see that this class contains many examples of groups that contain graph sequences of large…

The Guillemin-Sternberg conjecture states that "quantisation commutes with reduction" in a specific technical setting. So far, this conjecture has almost exclusively been stated and proved for compact Lie groups $G$ acting on compact…

Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo…

Fuglede's conjecture states that for a subset $\Omega$ of a locally compact abelian group $G$ with positive and finite Haar measure, there exists a subset of the dual group of $G$ which is an orthogonal basis of $L^{2}(\Omega)$ if and only…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…

We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…

We describe a geometric counterpart of the Baum-Connes map for the p-adic group GL(n).

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.