On the stability by tensor products of complexes of arithmetic D-modules

2006/05/04 by Daniel Caro, Caro, Daniel
Mathematics · #14F10 #14F30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14F10 #msc:14F30

paper · pdf · doi:10.48550/arxiv.math/0605125

arxiv created 2012/11/26 · arxiv updated 2012/11/27

Abstract

Let V be a complete discrete valued ring of mixed characteristic (0,p), K its field of fractions, k its residue field which is supposed to be perfect. Let X be a separated k-scheme of finite type and Y be a smooth open of X. We check that the equivalence of categories sp_(Y,X),+ (from the category of overconvergent isocrystals on (Y,X)/K to that of overcoherent isocrystals on (Y,X)/K) commutes with tensor products. Next, in Berthelot's theory of arithmetic D-modules, we prove the stability under tensor products of the devissability in overconvergent isocrystals. With Frobenius structures, we get the stability under tensor products of the overholonomicity.

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