Gauss-Manin connection and t-adic geometry

2008/06/10 by Johannes Nicaise, Nicaise, Johannes
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #advanced mathematical theories #math.AG

paper · pdf · doi:10.48550/arxiv.0806.1702

11 pages

arxiv created 2008/06/10 · openalex publication_date 2008/06/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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