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$p$-adic superspaces and Frobenius

A. Schwarz·I. Shapiro
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Abstract

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 $\zp$ (the ring of $p$-adic integers), as well as an alternative construction of the crystalline cohomology of a smooth projective variety over $\fp$ (finite field with $p$ elements).

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A. Schwarz, I. Shapiro. 2012-10-09. $p$-adic superspaces and Frobenius. https://arxiv.org/abs/math/0605310

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