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Sur la stabilité par produit tensoriel de complexes de \({\mathcal{D}}\)-modules arithmétiques

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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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Correspondence to Daniel Caro.

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L’auteur a bénéficié du soutien du réseau européen TMR Arithmetic Algebraic Geometry (contrat numéro UE MRTN-CT-2003-504917).

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Caro, D. Sur la stabilité par produit tensoriel de complexes de \({\mathcal{D}}\)-modules arithmétiques. manuscripta math. 147, 1–41 (2015). https://doi.org/10.1007/s00229-014-0716-4

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