Berkovich, Vladimir G. \(p\)-adic analytic spaces. (English) Zbl 0949.14010 Doc. Math. Extra Vol. ICM Berlin 1998, Vol. II, 141-151 (1998). 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. Cited in 2 Documents 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 Keywords:étale cohomology; vanishing cycles; \(p\)-adic analytic geometry; homotopy PDFBibTeX XMLCite \textit{V. G. Berkovich}, Doc. Math. Extra Vol., 141--151 (1998; Zbl 0949.14010) Full Text: EuDML EMIS