Duke Mathematical Journal

A p-adic nonabelian criterion for good reduction of curves

Fabrizio Andreatta, Adrian Iovita, and Minhyong Kim

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Abstract

Let K be a complete discrete valuation field of characteristic 0, with valuation ring OK and perfect residue field k of positive characteristic p. We prove that a proper and smooth curve over K, admitting a semistable model over OK, has good reduction if and only if its unipotent p-adic étale fundamental group is crystalline.

Article information

Source
Duke Math. J., Volume 164, Number 13 (2015), 2597-2642.

Dates
Received: 24 June 2013
Revised: 28 October 2014
First available in Project Euclid: 5 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1444051070

Digital Object Identifier
doi:10.1215/00127094-3146817

Mathematical Reviews number (MathSciNet)
MR3405595

Zentralblatt MATH identifier
1347.11051

Subjects
Primary: 11G20: Curves over finite and local fields [See also 14H25]
Secondary: 14F30: $p$-adic cohomology, crystalline cohomology 14G22: Rigid analytic geometry 14G32: Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)

Keywords
unipotent fundamental group p-adic Hodge theory

Citation

Andreatta, Fabrizio; Iovita, Adrian; Kim, Minhyong. A $p$ -adic nonabelian criterion for good reduction of curves. Duke Math. J. 164 (2015), no. 13, 2597--2642. doi:10.1215/00127094-3146817. https://projecteuclid.org/euclid.dmj/1444051070


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