Equivariant crystalline cohomology and base change

Equivariant Crystalline Cohomology and Base Change

Given a perfect field k of characteristic p > 0, a smooth proper k-scheme Y , a crystal E on Y relative to W (k) and a finite group G acting on Y and E, we show that, viewed as a virtual k[G]-module, the reduction modulo p of the crystalline cohomology of E is the de Rham cohomology of E modulo p. On the way we prove a base change theorem for the virtual Grepresentations associated with G-equiv...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

Equivariant Cohomology and Resolution

The ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...

Applications of Equivariant Cohomology

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic quotients and to indices of transversally elliptic operators. In particular,...