Related papers: On vanishing theorems for local systems associated…

We give a new algorithm computing local system cohomology groups for complexified real line arrangements. Using it, we obtain several conditions for the first local system cohomology to vanish and to be at most one-dimensional, which…

We show that in positive characteristic special loci of deformation spaces of rank one $\ell$-adic local systems are quasilinear. From this we deduce the Hard Lefschetz theorem for rank one $\ell$-adic local systems and a generic vanishing…

For all algebraic groups over non-Archimedean local fields, the bounded cohomology vanishes. This follows from the corresponding statement for automorphism groups of Bruhat--Tits buildings, which hinges on the solution to the flatmate…

We prove a Cohen-Dimca-Orlik type theorem for rank one $\mathbb{Z}$-local systems on complex hyperplane arrangement complements. This settles a recent conjecture of S. Sugawara.

We establish a "second vanishing theorem" for local cohomology modules over regular rings of unramified mixed characteristic, which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology. Applying this,…

The second vanishing theorem has a long history in the theory of local cohomology modules, which connects the vanishing of a complete regular local ring with a topological property of the punctured spectrum of the ring under some…

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

In this paper, we prove some well-known results on local cohomology with respect to a pair of ideals in graded version, such as, Independence Theorem, Lichtenbaum-Harshorne Vanishing Theorem, Basic Finiteness and Vanishing Theorem, among…

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…

Under the generic situation, the cohomology with the coefficients in the local system on complements of hypersurfaces vanishes except in the highest dimension. Our problem is of when the local system cohomology does not vanish. In the case…

The goal of this paper is twofold; on the one hand, motivated by questions raised by Schenzel, we explore situations where the Hartshorne--Lichtenbaum Vanishing Theorem for local cohomology fails, leading us to simpler expressions of…

Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles…

In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex K\"ahler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu's findings on…

Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative results concerning Artin vanishing for the cohomology of a Stein…

We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…

We establish a relative version of Gromov's Vanishing Theorem in the presence of amenable open covers with small multiplicity, extending a result of Li, L\"oh, and Moraschini. Our approach relies on Gromov's theory of multicomplexes.

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are…

We extend the techniques developed by Millson and Raghunathan to prove nonvanishing results for the cohomology of compact arithmetic quotients of hyperbolic n-space with values in the local coefficient systems associated to finite…

This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…

The main result of this work is a new proof and generalization of Lazard's comparison theorem of locally analytic group cohomology with Lie algebra cohomology for K-Lie groups, where K is a finite extension of the p-adic numbers. We show…