Overconvergent F-isocrystals and differential overcoherence

Details Overconvergent F-isocrystals and differential overcoherence Overconvergent F-isocrystals and differential overcoherence

2006-11-03

arxiv.org/abs/math/0611089v1

Mathematics

Algebraic Geometry

Scientific paper

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a smooth closed subscheme of $U$. We prove that the category of overconvergent $F$-isocrystals on $Y$ is equivalent to the category of overcoherent $F$-isocrystals on $Y$. More generally, we prove such an equivalence by gluing for any smooth variety $Y$ over $k$. Moreover, we check that overcoherent $F$-complexes of arithmetic $\mathcal{D}$-modules split in overconvergent $F$-isocrystals.

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