Semistable Lefschetz Pencils
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914043296481280 |
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| author | Esnault, Hélène Kerz, Moritz |
| author_facet | Esnault, Hélène Kerz, Moritz |
| contents | We study the geometry and cohomology of Lefschetz pencils for semistable schemes over a discrete valuation ring. We relate the global cohomological properties of the Lefschetz pencil and the monodromy-weight conjecture, in particular we show that if one assumes the monodromy-weight conjecture in smaller dimensions then one can obtain a rather complete understanding of the relative cohomology of the pencil. This reduces the monodromy-weight conjecture to an arithmetic variant of a conjecture of Kashiwara for the projective line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15886 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semistable Lefschetz Pencils Esnault, Hélène Kerz, Moritz Algebraic Geometry We study the geometry and cohomology of Lefschetz pencils for semistable schemes over a discrete valuation ring. We relate the global cohomological properties of the Lefschetz pencil and the monodromy-weight conjecture, in particular we show that if one assumes the monodromy-weight conjecture in smaller dimensions then one can obtain a rather complete understanding of the relative cohomology of the pencil. This reduces the monodromy-weight conjecture to an arithmetic variant of a conjecture of Kashiwara for the projective line. |
| title | Semistable Lefschetz Pencils |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2311.15886 |