Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-28T02:29:39.878Z Has data issue: false hasContentIssue false

Semistable reduction for overconvergent $F$-isocrystals I: Unipotence and logarithmic extensions

Published online by Cambridge University Press:  20 September 2007

Kiran S. Kedlaya
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA kedlaya@mit.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $X$ be a smooth variety over a field $k$ of characteristic $p>0$, and let $\mathcal{E}$ be an overconvergent isocrystal on $X$. We establish a criterion for the existence of a ‘canonical logarithmic extension’ of $\mathcal{E}$ to a smooth compactification $\overline{X}$ of $X$ whose complement is a strict normal crossings divisor. We also obtain some related results, including a form of Zariski–Nagata purity for isocrystals.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2007