相关论文: Higher Kazhdan projections and delocalised $\ell^ …

We establish new explicit zero-free regions for the Dedekind zeta-function. Two key elements of our proof are a non-negative, even, trigonometric polynomial and explicit upper bounds for the explicit formula of the so-called differenced…

Let $K$ be an extension of $\mathbb{Q}$ and $A/K$ an elliptic curve. If $\mathrm{Gal}(\bar K/K)$ is finitely generated, then $A$ is of infinite rank over $K$. In particular, this implies the $g=1$ case of the Junker-Koenigsmann conjecture.…

We consider generalized $\Lambda$-structures on algebras and schemes over the ring of integers $\mathit{O}_K$ of a number field $K$. When $K=\mathbb{Q}$, these agree with the $\lambda$-ring structures of algebraic K-theory. We then study…

We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite perspective enables us to control finite quotients and normal subgroups of these torsion…

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the…

The purpose of this note is to introduce a trick which relates the (non)-vanishing of the top-dimensional $\ell^2$-Betti numbers of actions with that of sub-actions. We provide three different types of applications: we prove that the…

We show that K_{2i}(Z[x,y]/(xy),(x,y)) is free abelian of rank 1 and that K_{2i+1}(Z[x,y]/(xy),(x,y)) is finite of order (i!)^2. We also compute K_{2i+1}(Z[x,y]/(xy),(x,y)) in low degrees.

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…

If K/F is a finite abelian Galois extension of global fields whose Galois group has exponent t, we prove that there exists a short exact sequence that has as a consequence that if t is square free, then Dec(K/F)=Br_{t}(K/F) which we use to…

We present a construction that produces infinite classes of K\"ahler groups that arise as fundamental groups of fibres of maps to higher dimensional tori. Following the work of Delzant and Gromov, there is great interest in knowing which…

We show that a large class of divisible abelian $\ell$-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the…

We apply a construction developed in a previous paper by the authors in order to obtain a formula which enables us to compute $\ell^2$-Betti numbers coming from a family of group algebras representable as crossed product algebras. As an…

For a recollement of derived module categories of rings, we provide sufficient conditions to guarantee the additivity formula of higher algebraic K-groups of the rings involved, and establish a long Mayer-Vietoris exact sequence of higher…

Given an elliptic self-adjoint pseudo-differential operator $P$ bounded from below, acting on the sections of a Riemannian line bundle over a smooth closed manifold $M$ equipped with some Lebesgue measure, we estimate from above, as $L$…

We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an application we construct a finitely…

We construct first examples of infinite groups having property (T) whose Kazhdan constants admit a lower bound independent of the choice of a finite generating set.

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These…

In this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values…

The first $\ell^2$ Betti number of a group is non-decreasing under various embeddings arising from first order logic. Strict inequality is proved for elementary embeddings of non-abelian proper subgroups within torsion free hyperbolic…

Let $\mathrm{R}$ be a real closed field. We prove that for any fixed $d$, the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of $\mathrm{R}^k$ defined by polynomials of degrees bounded by $d$ vanishes in…