# Notes on the motivic McKay correspondence for the group scheme $\alpha_{p}$

## TL;DR

This paper proposes a conjecture linking the motivic McKay correspondence for the group scheme α_p in characteristic p>0 with quotient varieties by α_p and cyclic groups of order p, supported by initial evidence.

## Contribution

It formulates a new conjecture relating the motivic McKay correspondence for α_p to quotient varieties by cyclic groups of order p in positive characteristic.

## Key findings

- Initial evidence supports the conjecture.
- Proposes a close relation between quotient varieties by α_p and cyclic groups.
- Lays groundwork for further research in motivic McKay correspondence in positive characteristic.

## Abstract

We formulate a conjecture on the motivic McKay correspondence for the group scheme $ \alpha_{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 $\alpha_{p}$ and ones by the cyclic group of order $p$.