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

• p-adic Hodge theory
• Étale cohomology, taking values over a ring of l-adic integers for l≠p