Supergeometry and Arithmetic Geometry
- Author(s): Schwarz, A.;
- Shapiro, I.
- et al.
Published Web Locationhttps://arxiv.org/pdf/hep-th/0605119.pdf
We 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.