TY - JOUR

T1 - Mass formulas for local Galois representations and quotient singularities II

T2 - Dualities and resolution of singularities

AU - Wood, Melanie Matchett

AU - Yasuda, Takehiko

N1 - Funding Information:
The authors would like to thank Kiran Kedlaya for helpful discussion. Yasuda thanks Max Planck Institute for Mathematics for its hospitality, where he stayed partly during this work. Wood was supported by NSF grants DMS-1147782 and DMS-1301690 and an American Institute of Mathematics Five Year Fellowship.
Publisher Copyright:
© 2017 Mathematical Sciences Publishers.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Dualities

KW - Equisingularities

KW - Local Galois representations

KW - Mass formulas

KW - Quotient singularities

KW - Stringy invariants

KW - The McKay correspondence

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U2 - 10.2140/ant.2017.11.817

DO - 10.2140/ant.2017.11.817

M3 - Article

AN - SCOPUS:85021383590

VL - 11

SP - 817

EP - 840

JO - Algebra and Number Theory

JF - Algebra and Number Theory

SN - 1937-0652

IS - 4

ER -