Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 13 (2015), 2597-2642.
A -adic nonabelian criterion for good reduction of curves
Let be a complete discrete valuation field of characteristic , with valuation ring and perfect residue field of positive characteristic . We prove that a proper and smooth curve over , admitting a semistable model over , has good reduction if and only if its unipotent -adic étale fundamental group is crystalline.
Duke Math. J., Volume 164, Number 13 (2015), 2597-2642.
Received: 24 June 2013
Revised: 28 October 2014
First available in Project Euclid: 5 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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