Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions
Number Theory
2024-02-27 v3 Algebraic Geometry
Abstract
We study a relation between the Artin conductor and the weight coming from the motivic integration over wild Deligne-Mumford stacks. As an application, we prove some version of the McKay correspondence, which relates Bhargava's mass formula for extensions of a local field and the Hilbert scheme of points.
Keywords
Cite
@article{arxiv.1309.2879,
title = {Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions},
author = {Melanie Machett Wood and Takehiko Yasuda},
journal= {arXiv preprint arXiv:1309.2879},
year = {2024}
}
Comments
22 pages, v.3: Section 5.1 was modified. Accordingly notation of (semi)rings was also modified in the rest of Section 5, to appear in International Mathematics Research Notices