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On the p-adic weight-monodromy conjecture for complete intersections in toric varieties

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arxiv 2207.00369 v2 pith:EN6V3FG6 submitted 2022-07-01 math.AG math.KTmath.NT

Federico Binda , Hiroki Kato , Alberto Vezzani This is my paper · ORCID
classification math.AGmath.KTmath.NT
keywords adiccompleteconjectureintersectionsprooftoricvarietiesadapt
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abstract

We give a proof of the $p$-adic weight monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze's proof in the $\ell$-adic setting, which we adapt using homotopical results developed in the context of rigid analytic motives.

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  1. A motivic approach to rational $p$-adic cohomologies

    math.AG 2025-08 conditional novelty 4.0 of 10

    Smooth complete intersections in projective toric varieties over p-adic fields satisfy the p-adic weight-monodromy conjecture, here re-proven through motivic nearby cycles and a monodromy-category equivalence.

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