Descent and generation for noncommutative coherent algebras over schemes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913689518473216 |
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| author | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali |
| author_facet | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali |
| contents | Our work shows forms of descent, in the fppf, h and étale topologies, for strong generation of the bounded derived category of a noncommutative coherent algebra over a scheme. Even for (commutative) schemes this yields new perspectives. As a consequence we exhibit new examples where these bounded derived categories admit strong generators. We achieve our main results by leveraging the action of the scheme on the coherent algebra, allowing us to lift statements into the noncommutative setting. In particular, this leads to interesting applications regarding generation for Azumaya algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Descent and generation for noncommutative coherent algebras over schemes De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali Algebraic Geometry Commutative Algebra Category Theory Rings and Algebras 14A22 (primary), 14A30, 14F08, 13D09 Our work shows forms of descent, in the fppf, h and étale topologies, for strong generation of the bounded derived category of a noncommutative coherent algebra over a scheme. Even for (commutative) schemes this yields new perspectives. As a consequence we exhibit new examples where these bounded derived categories admit strong generators. We achieve our main results by leveraging the action of the scheme on the coherent algebra, allowing us to lift statements into the noncommutative setting. In particular, this leads to interesting applications regarding generation for Azumaya algebras. |
| title | Descent and generation for noncommutative coherent algebras over schemes |
| topic | Algebraic Geometry Commutative Algebra Category Theory Rings and Algebras 14A22 (primary), 14A30, 14F08, 13D09 |
| url | https://arxiv.org/abs/2410.01785 |