[Un cas de conjecture de Hodge infinitésimale via un théorème de Hochschild–Kostant–Rosenberg pro]
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.
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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@article{CRMATH_2014__352_3_173_0,
author = {Morrow, Matthew},
title = {A case of the deformational {Hodge} conjecture via a pro {Hochschild{\textendash}Kostant{\textendash}Rosenberg} theorem},
journal = {Comptes Rendus. Math\'ematique},
pages = {173--177},
publisher = {Elsevier},
volume = {352},
number = {3},
year = {2014},
doi = {10.1016/j.crma.2014.01.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.01.008/}
}
TY - JOUR AU - Morrow, Matthew TI - A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem JO - Comptes Rendus. Mathématique PY - 2014 SP - 173 EP - 177 VL - 352 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.01.008/ DO - 10.1016/j.crma.2014.01.008 LA - en ID - CRMATH_2014__352_3_173_0 ER -
%0 Journal Article %A Morrow, Matthew %T A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem %J Comptes Rendus. Mathématique %D 2014 %P 173-177 %V 352 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.01.008/ %R 10.1016/j.crma.2014.01.008 %G en %F CRMATH_2014__352_3_173_0
Morrow, Matthew. A case of the deformational Hodge conjecture via a pro Hochschild–Kostant–Rosenberg theorem. Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 173-177. doi : 10.1016/j.crma.2014.01.008. http://www.numdam.org/articles/10.1016/j.crma.2014.01.008/
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