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Explicit resolution of weak wild quotient singularities on arithmetic surfaces

By Andrew Obus and Stefan Wewers

Abstract

A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed characteristic p fiber is a p-group acting with smallest possible ramification jump. In this paper, we give complete explicit resolutions of these singularities using deformation theory and valuation theory, taking a more local perspective than previous work has taken. Our descriptions answer several questions of Lorenzini. Along the way, we give a valuation-theoretic criterion for a normal snc-model of P^1 over a discretely valued field to be regular.Comment: Final version, to appear in the Journal of Algebraic Geometry. 31 page

Topics: Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, Mathematics - Number Theory, Primary: 11G20, 14B05, 14J17. Secondary: 13F30, 14B07, 14D15, 14H25
Year: 2019
OAI identifier: oai:arXiv.org:1805.09709

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