2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/181898We define a superspace over a ring $R$ as a functor on a subcategory of the category of supercommutative $R$-algebras. As an application the notion of a $p$-adic superspace is introduced and used to give a transparent construction of the Frobenius map on $p$-adic cohomology of a smooth projective variety over the ring of $p$-adic integers.14 pages, expanded introduction, more detailsHigh Energy Physics - TheoryAlgebraic Geometrytext