Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-23T04:12:02.623Z Has data issue: false hasContentIssue false

Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach

Published online by Cambridge University Press:  01 May 2008

Kiran S. Kedlaya*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA (email: [email protected])
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.

We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e. existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann–Zariski space associated to the function field of a variety. We also make some initial reductions, which allow attention to be focused on valuations of height 1 and transcendence degree 0.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The author was supported by NSF grant DMS-0400727.