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arXiv · 2201.06402

A note on the Gauss-Manin connection for abelian schemes

Tiago J. Fonseca·Nils Matthes
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Abstract

We study differential forms on the universal vector extension $A^\natural$ of an abelian scheme $A$ in characteristic zero, and derive a new construction of the $D$-group scheme structure on $A^\natural$. This gives, in particular, a rather simple description of the Gauss--Manin connection on the de Rham cohomology of $A$ in terms of global algebraic differential forms on $A^\natural$. The key ingredient is the computation of the coherent cohomology of $A^{\natural}$, due to Coleman and Laumon.

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Tiago J. Fonseca, Nils Matthes. 2022-01-17. A note on the Gauss-Manin connection for abelian schemes. https://arxiv.org/abs/2201.06402

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