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# Multi angle

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Multi angle de Rham theorem in non-Archimedean analytic geometry

Auteurs : Berkovich, Vladimir (Auteur de la Conférence)
CIRM (Editeur )

Résumé : In my work in progress on complex analytic vanishing cycles for formal schemes, I have defined integral "etale" cohomology groups of a compact strictly analytic space over the field of Laurent power series with complex coefficients. These are finitely generated abelian groups provided with a quasi-unipotent action of the fundamental group of the punctured complex plane, and they give rise to all $l$-adic etale cohomology groups of the space. After a short survey of this work, I will explain a theorem which, in the case when the space is rig-smooth, compares those groups and the de Rham cohomology groups of the space. The latter are provided with the Gauss-Manin connection and an additional structure which allow one to recover from them the "etale" cohomology groups with complex coefficients.

Codes MSC :
14F20 - Étale and other Grothendieck topologies and cohomologies
14F40 - de Rham cohomology
14G22 - Rigid analytic geometry
32P05 - Non-Archimedean complex analysis
32S30 - Deformations of singularities; vanishing cycles

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 06/04/17 Date de captation : 28/03/17 Collection : Research talks Format : MP4 Domaine : Algebraic & Complex Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2017-03-28_Berkovich.mp4 Informations sur la rencontre Nom du congrès : $p$-adic analytic geometry and differential equations / Géométrie analytique et équations différentielles $p$-adiquesOrganisteurs Congrès : Lebacque, Philippe ; Nicaise, Johannes ; Poineau, JérômeDates : 27/03/17 - 31/03/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1609.htmlCitation DataDOI : 10.24350/CIRM.V.19153703Cite this video as: Berkovich, Vladimir (2017). de Rham theorem in non-Archimedean analytic geometry.CIRM .Audiovisual resource. doi:10.24350/CIRM.V.19153703URI : http://dx.doi.org/10.24350/CIRM.V.19153703

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