Singular Hochschild cohomology via the singularity category

Bernhard Keller

doi:10.1016/j.crma.2018.10.003

Homological algebra/Algebraic geometry

Singular Hochschild cohomology via the singularity category
[La cohomologie de Hochschild singulière via la catégorie des singularités]

Présenté par : Michèle Vergne

Bernhard Keller ¹

¹ Université Paris-Diderot – Paris-7, Sorbonne Université, UFR de Mathématiques, CNRS, Institut de mathématiques de Jussieu–Paris Rive gauche, IMJ–PRG, bâtiment Sophie-Germain, 75205 Paris cedex 13, France

Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1106-1111.

est référencé par Corrections to “Singular Hochschild cohomology via the singularity category” [C. R. Acad. Sci. Paris, Ser. I 356 (2018) 1106–1111]
[Corrigendum à « La cohomologie de Hochschild singulière via la catégorie des singularités » [C. R. Acad. Sci. Paris, Ser. I 356 (2018) 1106–1111]]

Résumé
Abstract

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.

Reçu le : 2018-09-14
Accepté le : 2018-10-22
Publié le : 2018-10-25

DOI : 10.1016/j.crma.2018.10.003

Affiliations des auteurs :

Bernhard Keller ¹

¹ Université Paris-Diderot – Paris-7, Sorbonne Université, UFR de Mathématiques, CNRS, Institut de mathématiques de Jussieu–Paris Rive gauche, IMJ–PRG, bâtiment Sophie-Germain, 75205 Paris cedex 13, France

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Bernhard Keller. Singular Hochschild cohomology via the singularity category. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1106-1111. doi : 10.1016/j.crma.2018.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.10.003/

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