nLab
syntomic cohomology

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Cohomology

cohomology

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Idea

Syntomic cohomology is the abelian sheaf cohomology of the syntomic site of a scheme. It is a pp-adic analogue of Deligne-Beilinson cohomology.

It is closely related to the crystalline cohomology of that scheme. It may be regarded as a pp-adic absolute Hodge cohomology.

References

The syntomic site was introduced in

  • Jean-Marc Fontaine and William Messing, pp-Adic periods and pp-adic etale cohomology (pdf)

Further developments are in

  • Amnon Besser, Syntomic regulators and pp-adic integration I: rigid syntomic regulators (pdf)

The following shows that, just as Deligne-Beilinson cohomology may be interpreted as absolute Hodge cohomology, syntomic cohomology may be interpreted as pp-adic absolute Hodge cohomology.

Revised on September 12, 2015 10:40:13 by Adeel Khan (77.9.44.113)