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The Gauss-Manin connection on the Hodge structures

M. Rovinsky
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Abstract

Pour tout schéma simplicial complexe $X_{\bullet}$ il existe une application canonique $\nabla:H^{\ast}(X_{\bullet})\longrightarrow Ω^1_{{\mathbb C}/{\mathbb Q}}\otimes H^{\ast}(X_{\bullet})$, appelée la connexion de Gauß-Manin. Nous montrons qu'il existe une unique connexion fonctorielle sur toute structure de Hodge-Tate mixte ayant certaines propriétés de la connexion de Gauß-Manin. Cette connexion n'est pas intégrable en général, et alors son intégrabilité est une condition non triviale pour qu'une structure de Hodge soit géométrique. Dans des cas particuliers, je donne des formules explicites pour la connexion de Gauß-Manin sur la cohomologie singulière des variétés algébriques sur ${\mathbb C}$ dans les termes de la structure de Hodge.

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M. Rovinsky. 2001-01-18. The Gauss-Manin connection on the Hodge structures. https://doi.org/10.1016/s0764-4442(01)02064-x

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