Timeline for Galois Cohomology and $\sqrt{k} \notin \mathbb{Q}$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2017 at 14:32 | comment | added | john mangual | supplement: 28 proofs of the irrationality of $\sqrt{2}$ | |
| Jun 10, 2017 at 14:00 | comment | added | LSpice | Certainly $\sqrt2 \not\in \mathbb Q_2$, because $\mathrm{ord}_2(2) = 1$ and $\mathrm{ord}$ is $\mathbb Z$-valued on $\mathbb Q_2$. I'm not sure if it's what you have in mind, but there is an identification $\mathbb Q^\times/(\mathbb Q^\times)^2 \cong \mathrm H^1(\mathbb Q, \mu_2)$ sending $k \mapsto (\sigma \mapsto (\sigma - 1)\sqrt k)$, that is, sending a square class to the coboundary in $\mathrm GL_1$ corresponding to either square root, which is necessarily $\mu_2$-valued. | |
| Jun 10, 2017 at 13:58 | comment | added | Jason Starr | There is an excellent book on Galois cohomology by Serre. | |
| Jun 10, 2017 at 13:52 | history | asked | john mangual | CC BY-SA 3.0 |