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- W4300686988 abstract "Hesselholt defined a spectrum $operatorname{TP}(X)$, the periodic topological cyclic homology of a scheme $X$, using topological Hochschild homology and the Tate construction, which is a topological analogue of Connes-Tsygan periodic cyclic homology $operatorname{HP}$ defined by Hochschild homology and the Tate construction. Goodwillie proved that for $R$ an algebra over a field of characteristic 0 and $I$ a nilpotent ideal of $R$, the quotient map $Rto R/I$ induces an isomorphism on $operatorname{HP}$. In this paper, we show that the analogous result for $operatorname{TP}$ does not hold, that is to say, there is an algebra of positive characteristic and a nilpotent ideal such that the quotient map does not induce an isomorphism on $operatorname{TP}$, even rationally." @default.
- W4300686988 created "2022-10-04" @default.
- W4300686988 creator A5033090466 @default.
- W4300686988 date "2017-12-08" @default.
- W4300686988 modified "2023-09-27" @default.
- W4300686988 title "The non-nil-invariance of TP" @default.
- W4300686988 doi "https://doi.org/10.48550/arxiv.1712.03187" @default.
- W4300686988 hasPublicationYear "2017" @default.
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