The Atiyah class on algebraic stacks
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866916487387676672 |
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| author | Kuhn, Nikolas |
| author_facet | Kuhn, Nikolas |
| contents | We generalize Illusie's definition of the Atiyah class to complexes with quasi-coherent cohomology on arbitrary algebraic stacks. We show that this gives a global obstruction theory for moduli stacks of complexes in algebraic geometry without derived methods. We give a similar generalization of the reduced Atiyah class, and show various useful properties for working with Atiyah classes, such as compatibilities between the reduced and ordinary Atiyah class, and compatibility with tensor products and determinants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13934 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Atiyah class on algebraic stacks Kuhn, Nikolas Algebraic Geometry 14A30 (Primary) 14D20, 14B10 (Secondary) We generalize Illusie's definition of the Atiyah class to complexes with quasi-coherent cohomology on arbitrary algebraic stacks. We show that this gives a global obstruction theory for moduli stacks of complexes in algebraic geometry without derived methods. We give a similar generalization of the reduced Atiyah class, and show various useful properties for working with Atiyah classes, such as compatibilities between the reduced and ordinary Atiyah class, and compatibility with tensor products and determinants. |
| title | The Atiyah class on algebraic stacks |
| topic | Algebraic Geometry 14A30 (Primary) 14D20, 14B10 (Secondary) |
| url | https://arxiv.org/abs/2306.13934 |