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Notes on the motivic McKay correspondence for the group scheme $α_{p}$

Fabio Tonini, Takehiko Yasuda

Abstract

We formulate a conjecture on the motivic McKay correspondence for the group scheme $ α_{p}$ in characteristic $p>0$ and give a few evidences. The conjecture especially claims that there would be a close relation between quotient varieties by $α_{p}$ and ones by the cyclic group of order $p$.

Notes on the motivic McKay correspondence for the group scheme $α_{p}$

Abstract

We formulate a conjecture on the motivic McKay correspondence for the group scheme in characteristic and give a few evidences. The conjecture especially claims that there would be a close relation between quotient varieties by and ones by the cyclic group of order .

Paper Structure

This paper contains 7 sections, 5 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Moduli of $G$ and $H$-torsors over the punctured formal disk.
  3. Motivic measures on $\Delta_{G}$ and $\Delta_{H}$
  4. A conjecture on the McKay correspondence for linear $G$-actions
  5. Two Examples
  6. The change of variables in dimension two
  7. Representation theory of $\alpha_{p}$

Key Result

Theorem 4.1

If $D_{\mathbf{d}}\ge2$, we have the following equalities in $\hat{\mathcal{M}}'\cup\{\infty\}$,

Theorems & Definitions (14)

  • Remark 2.1
  • Theorem 4.1
  • Lemma 4.2
  • proof
  • Conjecture 4.3
  • Remark 5.1
  • Lemma 6.1
  • proof
  • Theorem 6.2
  • Remark 6.3
  • ...and 4 more