The six-functor formalism for rigid analytic motives
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866911982978859008 |
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| author | Ayoub, Joseph Gallauer, Martin Vezzani, Alberto |
| author_facet | Ayoub, Joseph Gallauer, Martin Vezzani, Alberto |
| contents | We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_15004 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The six-functor formalism for rigid analytic motives Ayoub, Joseph Gallauer, Martin Vezzani, Alberto Algebraic Geometry Algebraic Topology K-Theory and Homology Number Theory We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry. |
| title | The six-functor formalism for rigid analytic motives |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology Number Theory |
| url | https://arxiv.org/abs/2010.15004 |