The Overconvergent Site II. Cohomology

Bernard Le Stum (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Cohomology; Rigid; Berkovich; Crystalline

Domaines: Géométrie algébrique [math.AG]

Bernard Le Stum. The Overconvergent Site II. Cohomology. 2007. ⟨hal-00162168⟩