The $l$-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910080131137536 |
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| author | Nakkajima, Yukiyoshi |
| author_facet | Nakkajima, Yukiyoshi |
| contents | For a family of log points with constant log structure and for a proper SNCL scheme with an SNCD over the family, we construct a fundamental l-adic bifiltered complex as a geometric application of the theory of the derived category of (bi)filtered complexes in our papers. By using this bifiltered complex, we give the formulation of the log l-adic relative monodromy-weight conjecture with respect to the filtration arising from the SNCD. That is, we state that the relative l-adic monodromy filtration should exist for the Kummer log etale cohomological sheaf of the proper SNCL scheme with an SNCD and it should be equal to the l-adic weight filtration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $l$-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD Nakkajima, Yukiyoshi Algebraic Geometry For a family of log points with constant log structure and for a proper SNCL scheme with an SNCD over the family, we construct a fundamental l-adic bifiltered complex as a geometric application of the theory of the derived category of (bi)filtered complexes in our papers. By using this bifiltered complex, we give the formulation of the log l-adic relative monodromy-weight conjecture with respect to the filtration arising from the SNCD. That is, we state that the relative l-adic monodromy filtration should exist for the Kummer log etale cohomological sheaf of the proper SNCL scheme with an SNCD and it should be equal to the l-adic weight filtration. |
| title | The $l$-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.00201 |