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Galois Seminar

Friday, December 1, 2017 - 3:15pm

Jim Phillips

University of Virginia


University of Pennsylvania

DRL 4N30

Given a branched cover of curves defined over a mixed-characteristic discretely valued field, one asks whether this cover has good reduction to characteristic p. This arises from a question concerning tame fundamental groups: we know that one has a surjection from the tame fundamental group of a curve to that of its reduction, and finding the kernel of this map amounts to determining which covers have good reduction. By analyzing the torsor structure of certain components of the reduction, we show that we indeed have good reduction in the case of a cover of an elliptic curve defined over a sufficiently small field and branched over a single point whose Galois group has a cyclic Sylow p-subgroup.

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