Berkovich Motives
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912839066714112 |
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| author | Scholze, Peter |
| author_facet | Scholze, Peter |
| contents | We construct a theory of (etale) Berkovich motives. This is closely related to Ayoub's theory of rigid-analytic motives, but works uniformly in the archimedean and nonarchimedean setting. We aim for a self-contained treatment, not relying on previous work on algebraic or analytic motives. Applying the theory to discrete fields, one still recovers the etale version of Voevodsky's theory. Two notable features of our setting which do not hold in other settings are that over any base, the cancellation theorem holds true, and under only minor assumptions on the base, the stable $\infty$-category of motivic sheaves is rigid dualizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Berkovich Motives Scholze, Peter Algebraic Geometry K-Theory and Homology Number Theory 14F42, 14F20, 14G22, 14G45 We construct a theory of (etale) Berkovich motives. This is closely related to Ayoub's theory of rigid-analytic motives, but works uniformly in the archimedean and nonarchimedean setting. We aim for a self-contained treatment, not relying on previous work on algebraic or analytic motives. Applying the theory to discrete fields, one still recovers the etale version of Voevodsky's theory. Two notable features of our setting which do not hold in other settings are that over any base, the cancellation theorem holds true, and under only minor assumptions on the base, the stable $\infty$-category of motivic sheaves is rigid dualizable. |
| title | Berkovich Motives |
| topic | Algebraic Geometry K-Theory and Homology Number Theory 14F42, 14F20, 14G22, 14G45 |
| url | https://arxiv.org/abs/2412.03382 |