2009/10/23 by Jean-Yves Étesse, Jean-Yves Etesse, Etesse, Jean-Yves
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14F20 #14F30 #14G22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F20 #msc:14F30 #msc:14G22
paper · pdf · doi:10.48550/arxiv.0910.4436
26 pages
arxiv created 2009/10/23 · openalex publication_date 2009/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Syntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Having defined syntomic cohomology with compact supports of an abelian sheaf G on a k-scheme X, we show that it coincides with etale cohomology with compact supports when G is a lisse sheaf. If moreover the convergent F-isocrystal associated to G comes from an overconvergent isocrystal E, then the rigid cohomology of E expresses as a limit of syntomic cohomologies: then the etale cohomology with compact supports of G is the fixed points of Frobenius acting on the rigid cohomology of E.