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.
A p-adic non-abelian criterion for good reduction of curves / F. Andreatta, A. Iovita, M. Kim. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 164:13(2015), pp. 2597-2642. [10.1215/00127094-3146817]
A p-adic non-abelian criterion for good reduction of curves
F. Andreatta;
2015
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.
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