霍赫希尔德同调参数化弯曲莫里塔变形

arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-07 DOI:arxiv-2406.04945

Alessandro Lehmann

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引用次数: 0

摘要

我们证明，如果允许曲线变形，[KL09] 中引入的莫里塔变形与 dg 代数的第二霍赫希尔德同调之间的经典映射就会变成双射。我们还证明，当一个双模块在各自的 1 派生范畴之间引起等价时，它恰恰会引起曲线变形的等价。这些结果以及 arXiv:2402.08660 解决了一阶变形的曲率问题。

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Hochschild cohomology parametrizes curved Morita deformations

We show that, if one allows for curved deformations, the canonical map introduced in [KL09] between Morita deformations and second Hochschild cohomology of a dg algebra becomes a bijection. We also show that a bimodule induces an equivalence of curved deformations precisely when it induces an equivalence between the respective 1-derived categories. These results, together with arXiv:2402.08660, solve the curvature problem for first order deformations.

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arXiv - MATH - K-Theory and Homology

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