Full faithfulness for overconvergent F-isocrystals

Details Full faithfulness for overconvergent F-isocrystals Full faithfulness for overconvergent F-isocrystals

2001-10-11

arxiv.org/abs/math/0110125v4

preprint; published version: in Geometric Aspects of Dwork Theory (Volume II), de Gruyter (Berlin), 2004, 819-835.

Mathematics

Algebraic Geometry

18 pages; v4: second refereed version, adds overconvergent analogue of Quillen-Suslin. To appear in Geometric Aspects of Dwork

Scientific paper

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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