2001/06/22 by Kiran S. Kedlaya, Kedlaya, Kiran S.
Mathematics · Physics and Astronomy · #14F30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #math.AG #msc:14F30
paper · pdf · doi:10.48550/arxiv.math/0106192
21 pages
arxiv created 2001/06/22 · openalex publication_date 2001/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
R. Crew conjectured that every overconvergent F-isocrystal over k((t)) (k a field of positive characteristic) is quasi-unipotent (equivalently, potentially semistable), and so has ``generic'' and ``special'' Newton polygons. It is easy to construct a Newton polygon for an arbitrary overconvergent F-crystal 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 F-crystal can be trivialized over a large auxiliary ring. In a subsequent preprint, we use this construction to prove the aforementioned conjecture.