Berkovich, Vladimir G.

$p$-adic analytic spaces

Doc. Math. (Bielefeld) Extra Vol. ICM Berlin 1998, Vol. II, 141-151 (1998)


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.

Mathematics Subject Classification

14G20, 32P05, 11G25, 14F20, 32C37


étale cohomology, vanishing cycles, $p$-adic analytic geometry, homotopy