Categorical traces and a relative Lefschetz-Verdier formula
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866929208923521024 |
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| author | Lu, Qing Zheng, Weizhe |
| author_facet | Lu, Qing Zheng, Weizhe |
| contents | We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local acyclicity is equivalent to dualizability and deduce that duality preserves local acyclicity. As another application of the category of cohomological correspondences, we show that the nearby cycle functor over a Henselian valuation ring preserves duals, generalizing a theorem of Gabber. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_08522 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Categorical traces and a relative Lefschetz-Verdier formula Lu, Qing Zheng, Weizhe Algebraic Geometry Category Theory 14F20 (Primary), 18M05, 18N10, 32S30 (Secondary) We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local acyclicity is equivalent to dualizability and deduce that duality preserves local acyclicity. As another application of the category of cohomological correspondences, we show that the nearby cycle functor over a Henselian valuation ring preserves duals, generalizing a theorem of Gabber. |
| title | Categorical traces and a relative Lefschetz-Verdier formula |
| topic | Algebraic Geometry Category Theory 14F20 (Primary), 18M05, 18N10, 32S30 (Secondary) |
| url | https://arxiv.org/abs/2005.08522 |