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arXiv · 2311.15886

Semistable Lefschetz Pencils

Hélène Esnault·Moritz Kerz
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Abstract

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.

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Hélène Esnault, Moritz Kerz. 2023-11-27. Semistable Lefschetz Pencils. https://arxiv.org/abs/2311.15886

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