Related papers: A Going-Down principle for ample groupoids and the…

The Bogomolov conjecture claims that a closed subvariety containing a dense subset of small points is a special kind of subvarieties. In the arithmetic setting over number fields, the Bogomolov conjecture for abelian varieties has already…

For an ample groupoid with torsion-free stabilizers, we construct a Chern character map going from the domain of the Baum-Connes assembly map of G to the groupoid homology groups of G with rational coefficients. As a main application,…

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…

In this thesis, we investigate the proof of the Baum-Connes Conjecture with Coefficients for a-$T$-menable groups. We will mostly and essentially follow the argument employed by N. Higson and G. Kasparov in the paper [Nigel Higson and…

In this article we study a coarse version of the $K$-theoretic Farrell--Jones conjecture we call coarse or bounded isomorphism conjecture. Using controlled category theory we are able to translate this conjecture for asymptotically faithful…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary…

For a large class of word hyperbolic groups G the cross product C^*-algebra arising from the action of G on its Gromov boundary is shown to satisfy Poincare duality in K-theory. This class strictly contains fundamental groups of compact,…

We give a new proof of the Kat\v{e}tov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued…

In the setting of von Neumann algebras, measurable quantum groupoids have successfully been axiomatized and studied by Enock, Vallin, and Lesieur, whereas in the setting of $C^{*}$-algebras, a similar theory of locally compact quantum…

Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…

For locally compact groups, we define an analogue to Yu's property A that he defined for discrete metric spaces. We show that our property A for locally compact groups agrees with Roe's notion of property A for proper metric spaces, defined…

The purpose of this paper is to link anisotropy properties of an algebraic group together with compactness issues in the topological group of its rational points. We nd equivalent conditions on a smooth ane algebraic group scheme over a…

We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hyperbolic plane in a piecewise manner by generators of the…

This paper continues our investigation into the question of when a homotopy $\omega = \{\omega_t\}_{t \in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of…

We contribute to the Malle conjecture on the number N (K, G, y) of finite Galois extensions E of some number field K of finite group G and of discriminant of norm |N K/Q (d E)| $\le$ y. We prove the lower bound part of the conjecture for…

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…

We study the local epsilon constant conjecture as formulated by Breuning. This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected…