\(p\)-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.


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
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