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arXiv · 1505.07577

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

Melanie Machett Wood·Takehiko Yasuda
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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.

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Melanie Machett Wood, Takehiko Yasuda. 2015-05-28. Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities. https://doi.org/10.2140/ant.2017.11.817

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