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

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

2006-05-04

arxiv.org/abs/math/0605125v3

Mathematics

Algebraic Geometry

Scientific paper

Let $Y$ be a separated and smooth $k$-scheme. We prove that the functor $\sp _{Y+}$, which gives an equivalence of categories between overconvergent $F$-isocrystals and overcoherent $F$-isocrystals, commutes with tensor products. This implies the stability by tensor products of the category of $F$-complexes that split into overconvergent $F$-isocrystals. In the case of curves, we check that the category of holonomic $F$-complexes is equal to the category of $F$-complexes that split into overconvergent $F$-isocrystals. So, we get the stability of holonomicity by tensor products over curves.

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