第二类Hochschild（上）同调Ⅰ
Hochschild (co)homology of the second kind I
摘要：
本文定义并研究了弯曲DG-范畴的第二类Hochschild（上）同调（也称为Borel-Moore霍赫希尔德同调和紧支撑的Hochschild上同调）。本文构造了B上的右CDG-模的第二类CDG-范畴B的Hochschild（上）同调与B上的右CDG-模的DG-范畴C的Hochschild（上）同调之间的同构.利用DG-范畴上DG-模的两类导出范畴，给出了DG-范畴的两类Hochschild（上）同调同构的充分条件，特别地，给出了一种对角CD-双模B的“对角分解”条件，保证了相应的DG-范畴C的两类Hochschild（上）同调同构.几类的例子进行了讨论。
英文摘要：
We define and study the Hochschild (co)homology of the second kind (known also as the Borel-Moore Hochschild homology and the compactly supported Hochschild cohomology) for curved DG-categories. An isomorphism between the Hochschild (co)homology of the second kind of a CDG-category B and the same of the DG-category C of right CDG-modules over B, projective and finitely generated as graded B-modules, is constructed. Sufficient conditions for an isomorphism of the two kinds of Hochschild (co)homology of a DG-category are formulated in terms of the two kinds of derived categories of DG-modules over it. In particular, a kind of "resolution of the diagonal" condition for the diagonal CDG-bimodule B over a CDG-category B guarantees an isomorphism of the two kinds of Hochschild (co)homology of the corresponding DG-category C. Several classes of examples are discussed.
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