Vol. 11, No. 4, 2017

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
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
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.

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
Milestones
Received: 19 June 2015
Accepted: 1 March 2017
Published: 18 June 2017
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