We give a quick proof of the fact that the relative de Rham cohomology groups HdRi(X/S) 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. © Springer Nature Switzerland AG 2024.
A motivic proof of the finiteness of the relative de Rham cohomology / A. Vezzani. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - (2024), pp. 1-6. [10.1007/s00013-024-02024-7]
A motivic proof of the finiteness of the relative de Rham cohomology
A. Vezzani
2024
Abstract
We give a quick proof of the fact that the relative de Rham cohomology groups HdRi(X/S) 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. © Springer Nature Switzerland AG 2024.
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