Related papers: Schottky Groups over Valuation Rings

We continue an investigation initiated by Consani-Marcolli of the relation between the algebraic geometry of p-adic Mumford curves and the noncommutative geometry of graph C*-algebras associated to the action of the uniformizing p-adic…

Using the quaternionic formalism for the description of the group of isometries of hyperbolic $5$-space we consider arithmetically defined $5$-dimensional hyperbolic manifolds which are non-compact but of finite volume. They arise from…

In these notes we construct a quantization functor, associating an Hilbert space H(V) to a finite dimensional symplectic vector space V over a finite field F_q. As a result, we obtain a canonical model for the Weil representation of the…

The cyclotomic trace provides a comparison of the algebraic K-theory spectrum and a pro-spectrum TR that is built from the cyclic fixed points of topological Hochschild homology. In a previous paper with Ib Madsen, we used this comparison…

We characterize those 1-ended word hyperbolic groups whose Gromov boundaries are homeomorphic to trees of graphs (i.e. to inverse limits of graphs that have particularly simple finitary descriptions). These are groups with the simplest…

We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree…

We present two explicit combinatorial constructions of finitely summable reduced "Gamma"-elements $\gamma_r\,\in\,KK(C^*_r(\Gamma),{\mathbb C})$ for any word-hyperbolic group $(\Gamma,S)$ and obtain summability bounds for them in terms of…

Let $T_1$ and $T_2$ be homogeneous trees of even degree $\ge 4$. A BM group $\Gamma$ is a torsion free discrete subgroup of $\aut (T_1) \times \aut (T_2)$ which acts freely and transitively on the vertex set of $T_1 \times T_2$. This…

$\lambda$-graph systems are labeled Bratteli diagram with shift operations. They present subshifts. Their matrix presentations are called symbolic matrix systems. We define skew products of $\lambda$-graph systems and study extensions of…

Let $G$ be an algebraic group and $\Gamma$ a finite subgroup of automorphisms of $G$. Fix also a possibly ramified $\Gamma$-covering $\widetilde{X} \to X$. In this setting one may define the notion of $(\Gamma,G)$-bundles over…

This paper lays out the foundations of graded $K$-theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potential tool for their classification. For a row-finite $k$-graph…

Let $G$ be a connected, absolutely almost simple, algebraic group defined over a finitely generated, infinite field $K$, and let $\Gamma$ be a Zariski dense subgroup of $G(K)$. We show, apart from some few exceptions, that the…

In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let $K$ be a real quadratic field and $\Om_K$ its ring of integers. Let $\Gamma$ be a congruence subgroup of $\SL_2(\Om_K)$…

Kaleidoscopic groups are a class of permutation groups recently introduced by Duchesne, Monod, and Wesolek. Starting with a permutation group $\Gamma$, the kaleidoscopic construction produces another permutation group $\mathcal{K}(\Gamma)$…

We study infinite groups interpretable in three families of valued fields: $V$-minimal, power bounded $T$-convex, and $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and that if $G$ is dp-minimal then it…

Let $K$ be a $\mathbb{Q}$-Clifford algebra associated to an $(n-1)$-ary positive definite quadratic form and let $\mathcal{O}$ be a maximal order in $K$. A Clifford-Bianchi group is a group of the form $\operatorname{SL}_2(\mathcal{O})$…

Tree-graded spaces are generalizations of R-trees. They appear as asymptotic cones of groups (when the cones have cut points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying…

The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit…

Given a finite group $\Gamma$ and a virtual character $\wt$ on it, we construct a Fock space and associated vertex operators in terms of representation ring of wreath products $\Gamma\sim S_n$. We recover the character tables of wreath…

Let G be the group of rational points of a semisimple algebraic group of rank 1 over a nonarchimedean local field. We improve upon Lubotzky's analysis of graphs of groups describing the action of lattices in G on its Bruhat-Tits tree…