$p$-adic analytic spaces

Abstract

This report is a review of results in $p$-adic analytic geometry based on a new notion of analytic spaces. We explain the definition of analytic spaces, basic ideas of étale cohomology for them, an application to a conjecture of Deligne on vanishing cycles, the homotopy description of certain analytic spaces, and a relation between the étale cohomology of an algebraic variety and the topological cohomology of the associated analytic space.