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

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 how general 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.

20 pages

References in corpus (2)

• The wild McKay correspondence and $p$-adic measures
• Wilder McKay correspondences

Cited by in corpus (8)

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• Wilder McKay correspondences
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• Moduli of formal torsors II
• Crepant resolutions of quotient varieties in positive characteristics and their Euler characteristics
• Moduli of formal torsors
• Open problems in the wild McKay correspondence and related fields
• Motivic versions of mass formulas by Krasner, Serre and Bhargava