Mass formulas for local Galois representations and quotient singularities II: Dualities and resolution of singularities

Wood, Melanie; Yasuda, Takehiko

doi:10.2140/ant.2017.11.817

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Mass formulas for local Galois representations and quotient singularities II: Dualities and resolution of singularities

Melanie Matchett Wood and Takehiko Yasuda

Vol. 11 (2017), No. 4, 817–840

DOI: 10.2140/ant.2017.11.817

Abstract

A total mass is the weighted count of continuous homomorphisms from the absolute Galois group of a local field to a finite group. In the preceding paper, the authors observed that in a particular example two total masses coming from two different weightings are dual to each other. We discuss the problem of how generally such a duality holds and relate it to the existence of simultaneous resolution of singularities, using the wild McKay correspondence and the Poincaré duality for stringy invariants. We also exhibit several examples.

A correction was submitted on 1 Apr 2019 and posted online on 28 May 2019.

Keywords

mass formulas, local Galois representations, quotient singularities, dualities, the McKay correspondence, equisingularities, stringy invariants

Mathematical Subject Classification 2010

Primary: 11S15

Secondary: 11G25, 14E15, 14E16

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Received: 19 June 2015

Accepted: 1 March 2017

Published: 18 June 2017

Correction posted: 28 May 2019

Authors

Melanie Matchett Wood
Department of Mathematics University of Wisconsin 480 Lincoln Drive Madison, WI 53705 United States American Institute of Mathematics 360 Portage Avenue Palo Alto, CA 94306 United States

Takehiko Yasuda
Department of Mathematics, Graduate School of Science Osaka University Toyonaka 560-0043 Japan

Vol. 11, No. 4, 2017