A $p$ -adic nonabelian criterion for good reduction of curves - Andreatta, F; Iovita, A; Kim, M (Duke University Press, 2015)
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.