A derived category approach to Kempf's vanishing theorem

TL;DR

This paper presents a new proof of Kempf's vanishing theorem using derived categories of coherent sheaves on flag varieties, providing a novel algebraic geometric approach.

Contribution

It introduces a derived category framework to prove Kempf's vanishing theorem, connecting algebraic geometry and representation theory in a new way.

Findings

Proof of Andersen-Haboush identity established

Derived categories used to analyze flag varieties

New perspective on Kempf's vanishing theorem

Abstract

We give a proof of the Andersen-Haboush identity that implies Kempf's vanishing theorem. Our argument is based on the structure of derived categories of coherent sheaves on flag varieties over $\mathbb Z$.