The Overconvergent Site II. Cohomology

Details The Overconvergent Site II. Cohomology The Overconvergent Site II. Cohomology

2007-07-12

arxiv.org/abs/0707.1809v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

We prove that rigid cohomology can be computed as the cohomology of a site analogous to the crystalline site. Berthelot designed rigid cohomology as a common generalization of crystalline and Monsky-Washnitzer cohomology. Unfortunately, unlike the former, the functoriality of the theory is not built-in. We defined somewhere else the "overconvergent site" which is functorially attached to an algebraic variety and proved that the category of modules of finite presentation on this ringed site is equivalent to the category of over- convergent isocrystals on the variety. We show here that their cohomology also coincides.

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