Purity of critical cohomology and Kac’s conjecture

Purity Reconsidered the Cohomology of Moduli Spaces

Convention: all base schemes will be in characteristic p. Writing k or we will assume k = k F p , respectively = F p. We will write X ! S for a p-divisible group over a base S (and sometimes will say \a family of p-divisible groups"), while we tend to write X when we consider a p-divisible group over a base eld (but we are not strict in this convention). Instead of \p-divisible group" one can a...

Notions of Purity and the cohomology of Quiver-moduli

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natura...

On Kontsevich’s Hochschild cohomology conjecture

Etale Cohomology and the Weil Conjecture

amalgamation (except for F3) and as HNN-extensions (except for Tl and F3); that they are SQ-universal; and that each contains a noncongruence subgroup. In the case of the Picard group F15 some of these results are not proved until Chapter 6, which is devoted entirely to the Picard group, and which in addition discusses many other aspects of it, such as its abelian, nilpotent and normal subgroup...

Cohomology Operations and the Deligne Conjecture

The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.