Bia{\l}ynicki-Birula decomposition for reductive groups in positive characteristic

TL;DR

This paper establishes the Bialynicki-Birula decomposition for Kempf monoids, including reductive groups in positive characteristic, extending previous results to a broader class of algebraic monoids.

Contribution

It proves the existence of Bialynicki-Birula decomposition for Kempf monoids, expanding the scope to include reductive groups in all characteristics.

Findings

Bialynicki-Birula decomposition exists for Kempf monoids.

Extension of previous decomposition results to positive characteristic.

Includes monoids with reductive unit groups.

Abstract

We prove the existence of Bialynicki-Birula decomposition for Kempf monoids, which is a large class that contains for example monoids with reductive unit group in all characteristics. This extends the existence statements from previous works of Alper-Hall-Rydh and Jelisiejew-Sienkiewicz.