Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Explicit resolution of weak wild quotient singularities on arithmetic surfaces


Authors: Andrew Obus and Stefan Wewers
Journal: J. Algebraic Geom. 29 (2020), 691-728
DOI: https://doi.org/10.1090/jag/745
Published electronically: December 6, 2019
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Abstract | References | Additional Information

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 $ \mathbb{P}^1$ over a discretely valued field to be regular.


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Additional Information

Andrew Obus
Affiliation: Baruch College, 1 Bernard Baruch Way, New York, New York 10010
Email: andrewobus@gmail.com

Stefan Wewers
Affiliation: Universität Ulm, Helmholzstraße 18, 89081 Ulm, Germany
Email: stefan.wewers@uni-ulm.de

DOI: https://doi.org/10.1090/jag/745
Received by editor(s): June 10, 2018
Received by editor(s) in revised form: March 5, 2019, and May 5, 2019
Published electronically: December 6, 2019
Additional Notes: The first author was supported by NSF Grant DMS-1602054
Article copyright: © Copyright 2019 University Press, Inc.