Timeline for Alternative definitions of Weibel's homotopy K-theory
Current License: CC BY-SA 4.0
5 events
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| Jan 6, 2020 at 13:49 | history | edited | Kolya Ivankov |
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| Jan 6, 2020 at 12:19 | comment | added | Kolya Ivankov | Thing is, I get this kind of theory as a byproduct of another construction, and it seems to be related to Cortinas-Thom bivariant algebraic theory $kk$, for which, given an $R$-aglebra $B$, one has $kk(E,B)\cong KH(B)$. I'm trying to prove the coincidence of my group with $KH_0$ via this sideway, but wonder if I'm inventing a bicycle by downgrading a jet fighter :) | |
| Jan 6, 2020 at 12:14 | comment | added | Kolya Ivankov | It is the naive approach - my rings are in general not commutative, so there is no way to build sheaves. Suspension in this terms is a particular $\Sigma$ fitting into the short exact sequence $\Sigma A \to A[t, t^{-1}] \xrightarrow{ev_1} A$. | |
| Jan 6, 2020 at 12:06 | comment | added | Denis Nardin | What kind of $\mathbb{A}^1$-homotopy are we talking about? Do you mean the $\mathbb{A}^1$-localization of the sheaf or are you just taking naive $\mathbb{A}^1$-classes? The second approach doesn't seem very likely to work out. And what do you mean by "suspension"? | |
| Jan 6, 2020 at 11:33 | history | asked | Kolya Ivankov | CC BY-SA 4.0 |