Cohomology of G-sheaves in positive characteristic

Abstract

Let X be a noetherian scheme defined over an algebraically closed field of positive characteristic p, and G be a finite group, of order divisible by p, acting on X. We introduce a refinement of the equivariant K-theory of X to take into account the information related to modular representation theory. As an application, in the 1-dimensional case, we generalize a modular Riemann-Roch theorem given by S.Nakajima, extending the link between Galois modules and wild ramification.

42 pages, two applications to Galois covers of curves in positive characteristic added, see the introduction. Definition 7.24 corrected