Related papers: K-theory of virtually poly-surface groups

Given a graph of groups $\mathcal{G} = (\Gamma, \{G_v\}, \{G_e\})$ with certain conditions on vertex groups and $G$ acts acylindrically on its Bass-Serre tree $T$. Let $H$ be a finitely generated subgroup of $G$. We prove the following…

We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic…

Let $A$ be an abelian variety over the function field $K$ of a curve over a finite field. We describe several mild geometric conditions ensuring that the group $A(K^{\rm perf})$ is finitely generated and that the $p$-primary torsion…

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

We prove the Farrell-Jones Conjecture for mapping class groups. The proof uses the Masur-Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmueller space. The proof is presented in…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…

We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.

We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verifies the reductivity statement predicted…

We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GL_n(Z).

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

In this paper, we prove the Farrell-Jones Conjecture for the solvable Baumslag-Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic…

Let $\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\mathcal E$ (which means that $\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all…

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…

Let $S$ be either a free group or the fundamental group of a closed hyperbolic surface. We show that if $G$ is a finitely generated residually-$p$ group with the same pro-$p$ completion as $S$, then two-generated subgroups of $G$ are free.…

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…

We show that the relative Farrell-Jones assembly map from the family of finite subgroups to the family of virtually cyclic subgroups for algebraic K-theory is split injective in the setting where the coefficients are additive categories…

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger…

The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…

We prove that hypersurfaces defined by irreducible square-free polynomials have rational singularities. As an easy consequence, we deduce that certain (possibly non-square-free) polynomials associated to pairs of square-free polynomials…

A strongly zero-dimensional topological group containing a closed subgroup of positive covering dimension is constructed.