DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 141-151

Vladimir G. Berkovich

Title: p-Adic Analytic Spaces

This report is a review of results in $p$-adic analytic geometry based on a new notion of analytic spaces. I'll explain the definition of analytic spaces, basic ideas of \'etale 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 \'etale cohomology of an algebraic variety and the topological cohomology of the associated analytic space.

1991 Mathematics Subject Classification: 14G20, 14F20, 11G25, 32P05, 32C37

Keywords and Phrases: $p$-adic analytic spaces, \'etale cohomology, vanishing cycles

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