Half-integrality of line bundles on partial flag schemes of classical Lie groups

TL;DR

This paper develops a Galois descent theory for equivariant line bundles on partial flag schemes of classical Lie groups, providing a classification framework that advances understanding of line bundle structures in algebraic geometry.

Contribution

It introduces a new Galois descent approach for equivariant line bundles and classifies these bundles on partial flag schemes of classical Lie groups.

Findings

Classification of equivariant line bundles on partial flag schemes.

Development of Galois descent theory for these bundles.

Application to standard $ extbf{Z}[1/2]$-forms of classical Lie groups.

Abstract

In this paper, we develop a theory of Galois descent for equivariant line bundles on partial flag schemes. In particular, we study computational aspects of the classification of descent data of equivariant line bundles attached to characters of parabolic subgroups. As an application, we classify equivariant line bundles on partial flag schemes of the standard $\mathbb{Z}\left[1/2\right]$-forms of classical Lie groups.