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Overholonomic arithmetical D-modules

Daniel Caro
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Abstract

Let $k$ be a perfect field of characteristic $p >0$, $U$ be a variety over $k$ and $F$ be a power of Frobenius. We construct the category of overholonomic arithmetical ($F$-)$\D$-modules over $U$ and the category of overholonomic ($F$-)complexes over $U$. We prove that overholonomic complexes over $U$ are stables by direct images, inverse images, extraordinary inverse images, extraordinary direct images, dual functors. Moreover, in the smooth case, we check that unit-root overconvergent $F$-isocrystals are overholonomic. In particular, they are holonomic.

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Daniel Caro. 2008-01-18. Overholonomic arithmetical D-modules. https://arxiv.org/abs/math/0502442

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