Witt affine Springer theory

TL;DR

This paper advances affine Springer theory into mixed characteristic by developing perfect stacks and proving flatness of the Chevalley morphism in the Witt vector context.

Contribution

It introduces a new framework of perfectly placid perfect stacks and establishes foundational dimension theory in the mixed characteristic setting.

Findings

Development of perfect stacks with dimension theory

Proof of flatness of the Chevalley morphism in Witt vectors

Extension of affine Springer theory to mixed characteristic

Abstract

This paper extends the affine Springer theory developed by Bouthier, Kazhdan, and the second author (see [BKV]) to the mixed characteristic case. In particular, we introduce a theory of perfectly placid perfect infinity stacks and establish their dimension theory. Furthermore, we prove that, in the Witt vector setting, the Chevalley morphism between arc spaces is flat.