Gauss-Manin connection and t-adic geometry

Details Gauss-Manin connection and t-adic geometry Gauss-Manin connection and t-adic geometry

2008-06-10

arxiv.org/abs/0806.1702v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

We show that the de Rham cohomology of any separated and smooth rigid variety over a field of Laurent series of characteristic zero carries a natural formal meromorphic connection, which we call the Gauss-Manin connection. We compare it with the Gauss-Manin connection of a proper and smooth variety over a curve, and with the Gauss-Manin connection of the Milnor fibration at an isolated complex hypersurface singularity.

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