Good reduction of three-point Galois covers

Andrew Obus

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arXiv · 1208.3909

Good reduction of three-point Galois covers

Andrew Obus

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Abstract

Michel Raynaud gave a criterion for a three-point G-cover f : Y \rightarrow X = P^1, defined over a p-adic field K, to have good reduction. In particular, if the order of a p-Sylow subgroup of G is p, and the number of conjugacy classes of elements of order p is greater than the absolute ramification index e of K, then f has potentially good reduction. We give a different proof of this criterion, which extends to the case where G has an arbitrarily large cyclic p-Sylow subgroup, answering a question of Raynaud. We then use the criterion to give a family of examples of three-point covers with good reduction to characteristic p and arbitrarily large p-Sylow subgroups.

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Andrew Obus. 2012-08-20. Good reduction of three-point Galois covers. https://arxiv.org/abs/1208.3909

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