2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159732This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.18 pages; v2: refereed version (minor changes only); to appear in the proceedings of the 2005 AMS Summer Research Institute in Algebraic GeometryAlgebraic GeometryNumber Theory14F30, 14F40text