通过奇点范畴的奇异 Hochschild 上同调
表示论
2020-09-10 v9 代数几何
K理论与同调
摘要
我们证明对于 bounded dg 导出范畴是光滑的 noetherian 代数 ,其奇异 Hochschild 上同调(=Tate–Hochschild 上同调)作为分次代数同构于 的 dg 奇点范畴的 Hochschild 上同调。Zhengfang Wang 近期的工作提示了这样一种同构的存在。
引用
@article{arxiv.1809.05121,
title = {Singular Hochschild cohomology via the singularity category},
author = {Bernhard Keller},
journal= {arXiv preprint arXiv:1809.05121},
year = {2020}
}
备注
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