Timeline for How to compute the periodic cyclic homology of this algebra
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2023 at 18:13 | comment | added | SashaP | @user41650 My mistake, I should have rather referenced Theorem 5.4.12 in the same section. | |
| Aug 22, 2023 at 18:01 | comment | added | math no more | @user41650 The reference sciencedirect.com/science/article/pii/0040938385900552 Theorem III.5.1 might do it. | |
| Aug 22, 2023 at 17:44 | comment | added | user41650 | @SashaP Thanks for the reference, but it seems that the examples in Loday's book is about $k[x]/x^2$ with $deg(x)=0$, but in my question, the $deg(x)=-1$, does this matter? | |
| Aug 20, 2023 at 20:50 | vote | accept | user41650 | ||
| Aug 20, 2023 at 17:46 | comment | added | math no more | @SashaP Thanks! I might also add a paper by Bhatt: arxiv.org/abs/1207.6193 | |
| Aug 20, 2023 at 16:01 | comment | added | SashaP | It could be remarked that it's not a coincidence that $HP(A)$ turns out to be equal to $HP(k)$, the periodic cyclic homology of the base field: it's a theorem of Goodwillie's that periodic cyclic homology in characteristic zero is invariant under nilpotent thickenings, and our $k[x]/x^2$ is a nilpotent thickening of $k$. As far as references go, this particular example is considered in Section 5.4 (especially, 5.4.14) of Loday's book 'Cyclic homology'. | |
| Aug 20, 2023 at 15:24 | history | edited | math no more | CC BY-SA 4.0 |
some clarification
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| Aug 20, 2023 at 12:10 | history | edited | math no more | CC BY-SA 4.0 |
added 46 characters in body
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| Aug 20, 2023 at 9:11 | history | answered | math no more | CC BY-SA 4.0 |