The p-cyclic McKay correspondence via motivic integration

Takehiko Yasuda

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

We study the McKay correspondence for representations of the cyclic group of order p in characteristic p. The main tool is the motivic integration generalized to quotient stacks associated to representations. Our version of the change of variables formula leads to an explicit computation of the stringy invariant of the quotient variety. A consequence is that a crepant resolution of the quotient variety (if any) has topological Euler characteristic p as in the tame case. Also, we link a crepant resolution with a count of Artin-Schreier extensions of the power series field with respect to weights determined by ramification jumps and the representation.

Original languageEnglish
Pages (from-to)1125-1168
Number of pages44
JournalCompositio Mathematica
Volume150
Issue number7
DOIs
Publication statusPublished - 2014 Jul 17
Externally publishedYes

Keywords

  • Artin-Schreier extension
  • McKay correspondence
  • motivic integration
  • positive characteristic
  • stringy invariant

ASJC Scopus subject areas

  • Algebra and Number Theory

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