A survey by Niziol on “p-adic motivic cohomology”.
Fontaine and Messing: p-adic periods and p-adic etale cohomology
Kurihara: A note on p-adic etale cohomology
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AG (Algebraic geometry)
Charp
arXiv:1102.1294 p-adic periods and derived de Rham cohomology from arXiv Front: math.NT by Alexander Beilinson We construct p-adic period map using derived de Rham cohomology of Illusie and give a simple proof of Fontaine’s C_{dR} conjecture.
Yamasita: p-adic étale cohomology and crystalline cohomology of open varieties
arXiv:1205.1753 Deligne’s conjecture on the Lefschetz trace formula for -torsion étale cohomology from arXiv Front: math.AG by Megumi Takata Deligne’s conjecture is the Lefschetz trace formula for correspondences defined over a finite field. In this paper, we prove an analogous statement of Deligne’s conjecture with respect to -torsion étale cohomology under certain conditions, where is the characteristic of the base field.
nLab page on p-adic etale cohomology