The Newton polygons of overconvergent Fcrystals
Abstract
R. Crew conjectured that every overconvergent Fisocrystal over k((t)) (k a field of positive characteristic) is quasiunipotent (equivalently, potentially semistable), and so has ``generic'' and ``special'' Newton polygons. It is easy to construct a Newton polygon for an arbitrary overconvergent Fcrystal that coincides with the generic Newton polygon for potentially semistable crystals. We give an analogous construction for the special Newton polygon, by showing that the Fcrystal can be trivialized over a large auxiliary ring. In a subsequent preprint, we use this construction to prove the aforementioned conjecture.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:math/0106192
 Bibcode:
 2001math......6192K
 Keywords:

 Algebraic Geometry;
 14F30
 EPrint:
 21 pages