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Swan conductors for p-adic differential modules. II Global variation

Part of: Algebraic number theory: local and $p$-adic fields (Co)homology theory

Published online by Cambridge University Press:  11 May 2010

Kiran S. Kedlaya
Kiran S. Kedlaya
Affiliation:
Department of Mathematics, Room 2-165, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA (kedlaya@mit.edu)
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Abstract

Using a local construction from a previous paper, we exhibit a numerical invariant, the differential Swan conductor, for an isocrystal on a variety over a perfect field of positive characteristic overconvergent along a boundary divisor; this leads to an analogous construction for certain p-adic and l-adic representations of the étale fundamental group of a variety. We then demonstrate some variational properties of this definition for overconvergent isocrystals, paying special attention to the case of surfaces.

Keywords

p-adic differential modulesSwan conductorsoverconvergent isocrystalswild ramification

MSC classification

Secondary: 11S15: Ramification and extension theory 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Issue 1 , January 2011 , pp. 191 - 224
Copyright
Copyright © Cambridge University Press 2010

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