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arXiv · 2508.17773

A motivic proof of the finiteness of relative de Rham cohomology

Alberto Vezzani
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Abstract

We give a quick proof of the fact that the relative de Rham cohomogy groups of a smooth and proper map X/S between schemes over Q are vector bundles on the base, replacing Hodge-theoretic and transcendental methods with A1-homotopy theory

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Alberto Vezzani. 2025-08-25. A motivic proof of the finiteness of relative de Rham cohomology. https://doi.org/10.1007/s00013-024-02024-7

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