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comparison theorem (crystalline cohomology)

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Cohomology

cohomology

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Idea

A comparison between p-adic cohomology for varieties in characteristic p>0p \gt 0 and crystalline cohomology was was discussed in

  • Pierre Berthelot, Cohomologie cristalline des schémas de caractéristique g>0g \gt 0, Lecture Notes in Mathematics, Vol. 407, Springer- Verlag, Berlin, 1974. MR 0384804

The comparison theorem shown there (theorem V2.3.2) says that the crystalline cohomology over /p\mathbb{Z}/p is canonically identified with the de Rham cohomology of a lift to p-adic geometry if one exists.

Discussion of this in terms of Cech cohomology is in

Last revised on November 22, 2013 at 07:28:09. See the history of this page for a list of all contributions to it.