Semiorthogonal decompositions for generalized Severi-Brauer schemes
Ajneet Dhillon, Sayantan Roy Chowdhury
TL;DR
This paper develops semiorthogonal decompositions for generalized Severi-Brauer schemes and related homogeneous varieties, extending known results to more general bases and flag varieties using conservative descent.
Contribution
It introduces a method to produce semiorthogonal decompositions for derived categories of generalized Severi-Brauer schemes over arbitrary bases, generalizing previous results.
Findings
Semiorthogonal decomposition for generalized Severi-Brauer schemes.
Extension of Kapranov's results to flag varieties over arbitrary bases.
Application of conservative descent in derived category analysis.
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.
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Taxonomy
TopicsNonlinear Waves and Solitons