Unipotency and semistability of overconvergent F-crystals

Details Unipotency and semistability of overconvergent F-crystals Unipotency and semistability of overconvergent F-crystals

2001-02-21

arxiv.org/abs/math/0102173v2

Mathematics

Algebraic Geometry

24 pages; typos corrected, notation modified

Scientific paper

In this paper (part of the author's PhD thesis), we introduce the notions of semistability and potential semistability of overconvergent F-crystals over an equal characteristic local field. We establish their equivalence with the notions of unipotency and quasi-unipotency given by Crew, and to recast the conjecture that every overconvergent crystal is quasi-unipotent in terms of potential semistability. Consequences, including an extension of de Jong's extension theorem for F-crystals to the logarithmic case, will appear in a subsequent paper.

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