The six-functor formalism for rigid analytic motives
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 devel...
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| Veröffentlicht in: | Forum of mathematics. Sigma 2022-01, Vol.10, Article e61 |
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| container_title | Forum of mathematics. Sigma |
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| creator | Ayoub, Joseph Gallauer, Martin Vezzani, Alberto |
| description | 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. |
| doi_str_mv | 10.1017/fms.2022.55 |
| format | Article |
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| ispartof | Forum of mathematics. Sigma, 2022-01, Vol.10, Article e61 |
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| language | eng |
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| source | Cambridge Journals Open Access; DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Algebra Algebraic and Complex Geometry Algebraic Geometry Analytic geometry Formalism Geometry Mathematical analysis Mathematics Questions Theorems |
| title | The six-functor formalism for rigid analytic motives |
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