Explicit resolution of weak wild quotient singularities on arithmetic surfaces
Algebraic Geometry
2020-08-20 v3 Commutative Algebra
Number Theory
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.
Cite
@article{arxiv.1805.09709,
title = {Explicit resolution of weak wild quotient singularities on arithmetic surfaces},
author = {Andrew Obus and Stefan Wewers},
journal= {arXiv preprint arXiv:1805.09709},
year = {2020}
}
Comments
Final version, to appear in the Journal of Algebraic Geometry. 31 pages