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

Daniel Caro

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

Daniel Caro

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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 $\mathcal{D}$-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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Daniel Caro. 2012-11-26. On the stability by tensor products of complexes of arithmetic D-modules. https://arxiv.org/abs/math/0605125

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