基于箍缩复合体的Tate（co）同调
Tate (co)homology via pinched complexes
摘要：
对于模的复形，我们研究了两种新的构造，我们称之为捏张量积和捏Hom。它们为计算Tate同调和Tate上同调提供了新的方法，从而给出了结合环上模的Tate（上）同调的平衡性的概念性证明.我们考虑的另一个应用是局部代数。在Tate（上）同调为零的条件下，两个极小完全归结的压缩张量积得到一个极小完全归结。
英文摘要：
For complexes of modules we study two new constructions, which we call the pinched tensor product and the pinched Hom. They provide new methods for computing Tate homology and Tate cohomology, which lead to conceptual proofs of balancedness of Tate (co)homology for modules over associative rings. Another application we consider is in local algebra. Under conditions of vanishing of Tate (co)homology, the pinched tensor product of two minimal complete resolutions yields a minimal complete resolution.
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