Singular Hochschild cohomology via the singularity category
Representation Theory
2020-09-10 v9 Algebraic Geometry
K-Theory and Homology
Abstract
We show that for a noetherian algebra whose bounded dg derived category is smooth, the singular Hochschild cohomology (=Tate--Hochschild cohomology) is isomorphic, as a graded algebra, to the Hochschild cohomology of the dg singularity category of . The existence of such an isomorphism is suggested by recent work of Zhengfang Wang.
Keywords
Cite
@article{arxiv.1809.05121,
title = {Singular Hochschild cohomology via the singularity category},
author = {Bernhard Keller},
journal= {arXiv preprint arXiv:1809.05121},
year = {2020}
}
Comments
v4: 7 pages, statement of Lemma 2.4 corrected, v5: error at the beginning of the proof of Theorem 1.1 corrected, v6: commutative ground ring re-established, v7: Proof of Theorem 1.3 expanded and corrected, v8: references corrected, v9: Smoothness hypothesis added following a counterexample by Xiao-Wu Chen, v10: Hyp. on finite gldim of ground ring added following a remark by Xiao-Wu Chen