Exponential sums and rigid cohomology

In this article, we prove a comparison theorem between the Dwork cohomology introduced by Adolphson and Sperber and the rigid cohomology. As a corollary, we can calculate the rigid cohomology of Dwork isocrystal on torus.     

On a conjecture of Lynch

Abstract

We comment on a conjecture of Lynch on annihilators of local cohomology.

Communicated by Lawrence Ein     

On Hom-Lie antialgebra

Abstract

In this paper, we introduced the notion of Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in one-to-one correspondence to elements of the second cohomology group. We also prove that 1-parameter infinitesimal deformation of a Hom-Lie antialgebra are characterized by 2-cocycles of this Hom-Lie antialgebra with adjoint representation in itself. The notion of Nijenhuis operators of Hom-Lie antialgebra is introduced to describe trivial deformations.

Communicated by Dr. Pavel Kolesnikov     

On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers

Let (R,𝔪) be a local ring and I an ideal. The aim of the present paper is twofold. At first we continue the investigation to compare fgrade(I,R) with depth R∕I and further we derive some results on the vanishing of Lyubeznik numbers.