On affine Deligne-Lusztig varieties for <i>GL_n</i>

Abstract

In the first part of this thesis we study the global structure of moduli spaces of quasi-isogenies of p-divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components and of irreducible components. If the isocrystals of the p-divisible groups are simple, we compute the cohomology of the moduli space. As an application we determine which moduli spaces are smooth. <br /> In the second part we generalise some of these results to affine Deligne-Lusztig varieties for the general linear group. We describe the set of connected components of closed affine Deligne-Lusztig varieties and determine which of these varieties are zero-dimensional.