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arXiv · 2504.00201

The $l$-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD

Yukiyoshi Nakkajima
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Abstract

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.

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Yukiyoshi Nakkajima. 2026-03-29. The $l$-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD. https://arxiv.org/abs/2504.00201

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