Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions

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.

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

References in corpus (3)

• The $p$-cyclic McKay correspondence via motivic integration
• Toward motivic integration over wild Deligne-Mumford stacks
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities

Cited by in corpus (14)

• The wild McKay correspondence and $p$-adic measures
• Toward motivic integration over wild Deligne-Mumford stacks
• Wilder McKay correspondences
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities
• Inversion of adjunction for quotient singularities
• The Wild McKay Correspondence for Cyclic Groups of Prime Power Order
• Motivic Zeta Functions on $\mathds{Q}$-Gorenstein Varieties
• Moduli of formal torsors II
• Motivic integration over wild Deligne-Mumford stacks
• The v-function in the wild McKay correspondence is not determined by the ramification filtration
• Moduli of formal torsors
• Open problems in the wild McKay correspondence and related fields
• Motivic versions of mass formulas by Krasner, Serre and Bhargava
• Euler characteristic of crepant resolutions of specific modular quotient singularities