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arXiv · 2508.16196

A motivic approach to rational $p$-adic cohomologies

Federico Binda·Alberto Vezzani
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Abstract

We survey over some recent applications of motivic homotopy theory in the definition and the study of $p$-adic cohomology theories. In particular, we revisit the proof of the $p$-adic weight-monodromy conjecture for smooth projective hypersurfaces in light of the motivic definition of nearby cycles and monodromy operators.

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Federico Binda, Alberto Vezzani. 2025-08-22. A motivic approach to rational $p$-adic cohomologies. https://arxiv.org/abs/2508.16196

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