Related papers: Vanishing theorems for Shimura varieties at unipot…

Let $K$ be a finite extension of $\mathbb{Q}_p$ and $X$ a smooth proper $K$-variety with good reduction. Under a mild assumption on the behaviour of Hodge numbers under reduction modulo $p$, we prove that the existence of a non-zero global…

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, this theorem is generalized to…

In the present paper, we establish a general Kawamata-Viehweg-Koll\'ar-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact K\"ahler manifolds, unifying a number of…

In this article we prove several level lowering results for cuspidal automorphic representations occurring in the cohomology of the Siegel modular threefold with paramodular level structure by adapting a method of Ribet in his proof of the…

We construct a generalization of the Hasse invariant for certain unitary Shimura varieties of PEL type whose vanishing locus is the complement of the so-called \mu-ordinary locus. We show that the \mu-ordinary locus of those varieties is…

In this paper, for any Shimura datum $(G,\mathcal{D})$ satisfying reasonable conditions so that many interesting cases satisfy, we prove some finiteness theorems for any graded vector space consisting of automorphic forms on $\mathcal{D}$…

It is well-known that the point cohomology of the convolution algebra $\ell^1({\mathbb Z}_+)$ vanishes in degrees 2 and above. We sharpen this result by obtaining splitting maps whose norms are bounded independently of the choice of point…

We determine the Galois representations inside the $l$-adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to…

We show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and…

We prove a relative Kawamata Viehweg vanishing type theorem for birational morphisms. We use this to prove a Grauert Riemenschneider theorem over log canonical threefolds without zero dimensional log canonical centers, in residue…

Given a group satisfying sufficient finiteness properties, we discuss a group algebra criterion for vanishing of all its cohomology groups with unitary coefficients in a certain degree.

We extend the results of generic vanishing theory to polarizable real Hodge modules on compact complex tori, and from there to arbitrary compact K\"ahler manifolds. As applications, we obtain a bimeromorphic characterization of compact…

Looijenga's vanishing theorem on the moduli space of curves $M_g$ says that the tautological ring vanishes above degree $g-2$. We prove an analogous result for the tautological cohomology ring of the moduli space of K3 surfaces.

We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also…

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for…

Let G be a group of type FP_n and let p>1. In this paper we show that the reduced l^p-homology of G is dual to the reduced l^q-cohomology for \frac{1}{p}+\frac{1}{q}=1. In our main theorem we show that for a group of type FP_n with a…

Let $\Gamma_n(p)$ be the level-$p$ principal congruence subgroup of $\text{SL}_n(\mathbb{Z})$. Borel-Serre proved that the cohomology of $\Gamma_n(p)$ vanishes above degree $\binom{n}{2}$. We study the cohomology in this top degree…

We show a homological result for the class of planar or symmetric operad groups: We show that under certain conditions, group (co)homology of such groups with certain coefficients vanishes in all dimensions, provided it vanishes in…

We determine the Galois representations inside the $l$-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm…

We prove vanishing results of the cohomology groups of Aomoto complex over arbitrary coefficient ring for real hyperplane arrangements. The proof is using minimality of arrangements and descriptions of Aomoto complex in terms of chambers.…