2007/07/12 by Bernard Le Stum, Stum, Bernard Le
Mathematics · #14F30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0707.1809
openalex publication_date 2007/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.