[La cohomologie de Hochschild singulière via la catégorie des singularités]
Nous montrons que la cohomologie de Hochschild singulière (cohomologie de Tate–Hochschild) d'une algèbre A est isomorphe, en tant qu'algèbre graduée, à la cohomologie de Hochschild de l'enrichissement différentiel gradué de la catégorie des singularités de A. L'existence d'un tel isomorphisme est suggérée par des travaux récents de Zhengfang Wang.
We show that the singular Hochschild cohomology (= Tate–Hochschild cohomology) of an algebra A is isomorphic, as a graded algebra, to the Hochschild cohomology of the differential graded enhancement of the singularity category of A. The existence of such an isomorphism is suggested by recent work by Zhengfang Wang.
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@article{CRMATH_2018__356_11-12_1106_0,
author = {Keller, Bernhard},
title = {Singular {Hochschild} cohomology via the singularity category},
journal = {Comptes Rendus. Math\'ematique},
pages = {1106--1111},
publisher = {Elsevier},
volume = {356},
number = {11-12},
year = {2018},
doi = {10.1016/j.crma.2018.10.003},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2018.10.003/}
}
TY - JOUR AU - Keller, Bernhard TI - Singular Hochschild cohomology via the singularity category JO - Comptes Rendus. Mathématique PY - 2018 SP - 1106 EP - 1111 VL - 356 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2018.10.003/ DO - 10.1016/j.crma.2018.10.003 LA - en ID - CRMATH_2018__356_11-12_1106_0 ER -
%0 Journal Article %A Keller, Bernhard %T Singular Hochschild cohomology via the singularity category %J Comptes Rendus. Mathématique %D 2018 %P 1106-1111 %V 356 %N 11-12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2018.10.003/ %R 10.1016/j.crma.2018.10.003 %G en %F CRMATH_2018__356_11-12_1106_0
Keller, Bernhard. Singular Hochschild cohomology via the singularity category. Comptes Rendus. Mathématique, Tome 356 (2018) no. 11-12, pp. 1106-1111. doi : 10.1016/j.crma.2018.10.003. http://archive.numdam.org/articles/10.1016/j.crma.2018.10.003/
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