On the cyclic homology of exact categories
On the cyclic homology of exact categories
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DOI：
10.1016/s0022-4049(97)00152-7
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发表时间：
1999-03
影响因子：
0.8
通讯作者：
B. Keller
中科院分区：
文献类型：
--
作者：
B. Keller
精确范畴的循环同调由McCarthy（1994）使用Waldhausen（1985）的方法定义。McCarthy的理论有许多理想的性质，最基本的是一致性，即当应用于代数上有限生成的射影模的范畴时，它专门研究代数的循环同调。然而，我们证明了McCarthy的理论不能同时兼容于局部化和在派生范畴中诱导等价的函子下的不变性。这就是我们引入一个新理论的动机，它拥有三个属性：可拓性、不变性和局域性。由于这些性质，新理论可以显式地计算许多类别的模块和轴。
The cyclic homology of an exact category was defined by McCarthy (1994) using the methods of Waldhausen (1985). McCarthy's theory enjoys a number of desirable properties, the most basic being the agreement property, i.e. the fact that when applied to the category of finitely generated projective modules over an algebra it specializes to the cyclic homology of the algebra. However, we show that McCarthy's theory cannot be both compatible with localizations and invariant under functors inducing equivalences in the derived category. This is our motivation for introducing a new theory for which all three properties hold: extension, invariance and localization. Thanks to these properties, the new theory can be computed explicitly for a number of categories of modules and sheaves.