A motivic proof of the finiteness of relative de Rham cohomology
arXiv:2508.17773 · doi:10.1007/s00013-024-02024-7
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
4 pages