In mathematics, p-adic cohomology means a cohomology theory for varieties of characteristic p whose values are modules over a ring of p-adic integers. Examples (in roughly historical order) include:
Serre's Witt vector cohomology Monsky–Washnitzer cohomology Infinitesimal cohomology Crystalline cohomology Rigid cohomology Prismatic cohomology Habiro cohomology
See also p-adic Hodge theory Étale cohomology, taking values over a ring of l-adic integers for l≠p