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Full faithfulness for overconvergent F-isocrystals

Kiran S. Kedlaya
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Abstract

Let X be a smooth variety over a field of characteristic p>0. We prove that the forgetful functor from the category of overconvergent F-isocrystals on X to the category of convergent F-isocrystals is fully faithful. The argument uses the quasi-unipotence theorem for overconvergent F-isocrystals (recently proved independently by Andre, Mebkhout, and the author; see math.AG/0110124), plus arguments of de Jong. In the process, we establish a theorem of Quillen-Suslin type (i.e., every finite projective module is free) over rings of overconvergent power series.

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Kiran S. Kedlaya. 2003-06-01. Full faithfulness for overconvergent F-isocrystals. https://arxiv.org/abs/math/0110125

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