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The non-nil-invariance of periodic topological cyclic homology
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-04-15 , DOI: 10.4310/hha.2020.v22.n2.a11
Ryo Horiuchi 1
Affiliation  

Periodic topological cyclic homology $\operatorname{TP}$ is a topological analogue of periodic cyclic homology $\operatorname{HP}$. It is known that, for R an algebra over a field of characteristic $0$ and $I$ a nilpotent ideal of $R$, the quotient map $R \to R/I$ induces an isomorphism on $\operatorname{HP}$. In this paper, we show that the analogous result for $\operatorname{TP}$ does not hold.

中文翻译:

周期拓扑循环同源性的非零不变性

周期性拓扑循环同源性$ \ operatorname {TP} $是周期性循环同源性$ \ operatorname {HP} $的拓扑类似物。众所周知,对于R在特征$ 0 $和$ I $的幂代数$ R $的域上的代数,商映射$ R \到R / I $会导致$ \ operatorname {HP} $ 。在本文中,我们表明$ \ operatorname {TP} $的相似结果不成立。
更新日期:2020-04-15
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