Abstract
Let \({\mathcal{V}}\) 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 \({\mathcal{D}}\) -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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