Comptes Rendus
Homological algebra/Algebraic geometry
Singular Hochschild cohomology via the singularity category
Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1106-1111.

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.

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.

Published online:
DOI: 10.1016/j.crma.2018.10.003

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
     author = {Bernhard Keller},
     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},
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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.

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