A motivic proof of the finiteness of relative de Rham cohomology

2025/08/25 by Vezzani, Alberto
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17773

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

Citations

• Categorical formal punctured neighborhood of infinity, I
• Solution algebras of differential equations and quasi-homogeneous varieties: a new differential Galois correspondence

Cited by

• A motivic approach to rational p-adic cohomologies

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