Log motivic nearby cycles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929354492084224 |
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| author | Park, Doosung |
| author_facet | Park, Doosung |
| contents | We define the log motivic nearby cycles functor. We show that this sends the motive of a proper smooth scheme over the fraction field of a DVR to the motive of the boundary of a log smooth model assuming absolute purity, which is unconditional in the equal characteristic case. In characteristic $0$, we show that the $\infty$-categories of motives over the standard log point and rigid analytic motives are equivalent, and we relate log motivic nearby cycles functor with Ayoub's motivic nearby cycles functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14083 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log motivic nearby cycles Park, Doosung Algebraic Geometry 14F42, 14A21 We define the log motivic nearby cycles functor. We show that this sends the motive of a proper smooth scheme over the fraction field of a DVR to the motive of the boundary of a log smooth model assuming absolute purity, which is unconditional in the equal characteristic case. In characteristic $0$, we show that the $\infty$-categories of motives over the standard log point and rigid analytic motives are equivalent, and we relate log motivic nearby cycles functor with Ayoub's motivic nearby cycles functor. |
| title | Log motivic nearby cycles |
| topic | Algebraic Geometry 14F42, 14A21 |
| url | https://arxiv.org/abs/2405.14083 |