A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem

Matthew Morrow

doi:10.1016/j.crma.2014.01.008

Algebraic geometry/Homological algebra

A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem

Presented by: Claire Voisin

Matthew Morrow ¹

¹ Hausdorff Center for Mathematics, Endenicher Allee 60, 53115 Bonn, Germany

Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 173-177.

Abstract
Résumé

Following ideas of Bloch, Esnault, and Kerz, we establish the deformational part of Grothendieck's variational Hodge conjecture for proper, smooth schemes over $K 〚 t 〛$ , where K is an algebraic extension of $Q$ . The main tool is a pro Hochschild–Kostant–Rosenberg theorem for Hochschild homology.

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 $K 〚 t 〛$ , où K est une extension algébrique de $Q$ . L'outil principal est un théorème de Hochschild–Kostant–Rosenberg pro pour l'homologie de Hochschild.

Received: 2013-10-14
Accepted: 2014-01-20
Published online: 2014-02-14

DOI: 10.1016/j.crma.2014.01.008

Author's affiliations:

Matthew Morrow ¹

¹ Hausdorff Center for Mathematics, Endenicher Allee 60, 53115 Bonn, Germany

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     author = {Matthew Morrow},
     title = {A case of the deformational {Hodge} conjecture via a pro {Hochschild{\textendash}Kostant{\textendash}Rosenberg} theorem},
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     pages = {173--177},
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Matthew Morrow. A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem. Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 173-177. doi : 10.1016/j.crma.2014.01.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.01.008/

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