We introduce an equivariant version of cyclic cohomology for Hopf module algebras. For any H-module algebra A, where H is a Hopf algebra with S2 = idH we define the cocyclic module C ♮ H(A) and we find its relation with cyclic cohomology of crossed product algebra A ⋊ H. We define K 0 (A), the equivariant K-theory group of A, and its pairing with cyclic and periodic cyclic cohomology of C H(A).

Introduction 2 1. Preliminaries on conformal algebras and modules 4 2. Basic definitions 9 3. Extensions and deformations 13 4. Homology 17 5. Exterior multiplication, contraction, and module structure 18 6. Cohomology of conformal algebras and their annihilation Lie algebras 19 6.1. Cohomology of the basic complex 19 6.2. Cohomology of the reduced complex 21 6.3. Cohomology of conformal algebr...

This paper finds its motivation in the pursuit of ideals whose local cohomology modules have maximal Hilbert functions. In [8], [9] we proved that the lexicographic (resp. squarefree lexicographic) ideal of a family of graded (resp. squarefree) ideals with assigned Hilbert function provides sharp upper bounds for the local cohomology modules of any of the ideals of the family. Moreover these bo...

Let Mm be the formal scheme which represents the functor of deformations of a one-dimensional formal module over F̄p equipped with a level-m-structure. By work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic étale cohomology of the generic fibre Mm of Mm realizes simultaneously the local Langlands and Jacquet-Langlands correspondences. The proofs given so far use Drinfeld...

We study cohomology with coefficients in a rank one local system on the complement of an arrangement of hyperplanes A. The cohomology plays an important role for the theory of generalized hypergeometric functions. We combine several known results to construct explicit bases of logarithmic forms for the only non-vanishing cohomology group, under some nonresonance conditions on the local system, ...

In [8] we introduced the notion of a local torus actions modeled on the standard representation (we call it a local torus action for simplicity), which is a generalization of a locally standard torus action. In this note we define a lifting of a local torus action to a principal torus bundle, and show that there is an obstruction class for the existence of liftings in the first cohomology of th...