Timeline for Cohomology classes coming from algebraic K-theory
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2023 at 1:21 | vote | accept | sdr | ||
| Aug 4, 2023 at 12:30 | answer | added | Oli Gregory | timeline score: 4 | |
| May 26, 2021 at 20:02 | comment | added | Geordie Williamson | In case someone stumbles over this question in the future, Gillet's "Comparing Algebraic and Topological $K$-Theory" is useful. In particular, from the introduction: "for $K_0$ the image is (conjecturally) described by the Hodge conjecture, while for higher $K$-theory, the image must be torsion." | |
| Sep 4, 2020 at 19:03 | comment | added | Oli Gregory | One obstruction is that the image of $K_{n}(X)$ lies in the "Hodge" part of the mixed Hodge structure, i.e. $\bigoplus W_{2i}H^{2i-n}(X,\mathbb{Q})\cap F^{i}H^{2i-n}(X,\mathbb{C})$. For example, if $X$ is proper then the image is zero as soon as $n>0$. | |
| Sep 4, 2020 at 17:03 | history | asked | sdr | CC BY-SA 4.0 |