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Comptes Rendus Mathématique
Volume 352, n° 3
pages 173-177 (mars 2014)
Doi : 10.1016/j.crma.2014.01.008
Received : 14 October 2013 ;  accepted : 20 January 2014
A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem
Un cas de conjecture de Hodge infinitésimale via un théorème de Hochschild–Kostant–Rosenberg pro
 

Matthew Morrow
 Hausdorff Center for Mathematics, Endenicher Allee 60, 53115 Bonn, Germany 

Abstract

Following ideas of Bloch, Esnault, and Kerz, we establish the deformational part of Grothendieck's variational Hodge conjecture for proper, smooth schemes over  , where K is an algebraic extension of  . The main tool is a pro Hochschild–Kostant–Rosenberg theorem for Hochschild homology.

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Résumé

En suivant des idées de Bloch, Esnault et Kerz, nous établissons la partie formelle de la conjecture de Hodge variationnelle pour les schémas propres et lisses sur  , où K est une extension algébrique de  . L'outil principal est un théorème de Hochschild–Kostant–Rosenberg pro pour l'homologie de Hochschild.

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