Semiorthogonal decompositions for generalized Severi-Brauer schemes
Algebraic Geometry
2024-05-02 v1
Abstract
The purpose of this paper is to use conservative descent to study semi-orthogonal decompositions for some homogeneous varieties over general bases. We produce a semi-orthogonal decomposition for the bounded derived category of coherent sheaves on a generalized Severi-Brauer scheme. This extends known results for Sever-Brauer varieties and Grassmanianns. We use our results to construct semi-orthogonal decompositions for flag varieties over arbitrary bases. This generalises a result of Kapranov.
Cite
@article{arxiv.2405.00580,
title = {Semiorthogonal decompositions for generalized Severi-Brauer schemes},
author = {Ajneet Dhillon and Sayantan Roy Chowdhury},
journal= {arXiv preprint arXiv:2405.00580},
year = {2024}
}