Semiorthogonal decompositions for generalized Severi-Brauer schemes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913338272776192 |
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| author | Dhillon, Ajneet Chowdhury, Sayantan Roy |
| author_facet | Dhillon, Ajneet Chowdhury, Sayantan Roy |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semiorthogonal decompositions for generalized Severi-Brauer schemes Dhillon, Ajneet Chowdhury, Sayantan Roy Algebraic Geometry 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. |
| title | Semiorthogonal decompositions for generalized Severi-Brauer schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.00580 |