Bad reduction of curves and ramification of étale path torsors

In this talk I will describe how aspects of the reduction type of a curve over a local field are described by the Galois action on its étale torsor of paths. The results described may be viewed as an 'oid-ification' of a theorem of Oda which says that bad reduction of a curve can be detected in the Galois action on its fundamental group. In the context of Kim's program, this is used to determine certain local constants that arise in equations for Selmer schemes.