# zbMATH — the first resource for mathematics

$$p$$-adic analytic spaces. (English) Zbl 0949.14010
Summary: 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.

##### MSC:
 14G20 Local ground fields in algebraic geometry 32P05 Non-Archimedean analysis 11G25 Varieties over finite and local fields 14F20 Étale and other Grothendieck topologies and (co)homologies 32C37 Duality theorems for analytic spaces
Full Text: