Moduli stacks of vector bundles and Frobenius morphisms

Abstract

We describe the action of the different Frobenius morphisms on the cohomology ring of the moduli stack of algebraic vector bundles of fixed rank and determinant on an algebraic curve over a finite field in characteristic p and analyse special situations like vector bundles on the projective line and relations with infinite Grassmannians.1991 Mathematics Subject ClassificationPrimary 14F35secondary 14H10Key words and phrasesVector bundles on curvesstacksl-adic cohomologyFrobenius morphisms