Timeline for Fixing error in a proof from "Central simple algebras and Galois cohomology"
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2020 at 22:28 | comment | added | Kimball | I guess Julian answered your question, but IIRC, I believe this book has errata posted online. | |
| Dec 9, 2020 at 3:38 | comment | added | Rita | @JulianRosen: Ah, that makes a lot of sense. Thanks! | |
| Dec 9, 2020 at 3:22 | comment | added | Julian Rosen | If $x_1,\ldots,x_{n^2}$ is a basis for $D$, we could identify $D\otimes \bar{k}$ with $\mathbb{A}^{n^2}_{\bar{k}}$ via $\sum x_i\otimes\lambda_i\mapsto (\lambda_i)_i$ (this identification is not the same as the one coming from an isomorphism $D\otimes \bar{k}\simeq M_n(\bar{k})$). With this identification, it is clear that $D$ is identified with $\mathbb{A}^{n^2}_k$, so $D\cap U\neq\varnothing$. | |
| Dec 9, 2020 at 2:29 | history | edited | Toby Bartels | CC BY-SA 4.0 |
typo, clarify edition (per comments)
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| Dec 9, 2020 at 1:38 | comment | added | Rita | @KReiser: I'm not sure I follow. Why must $D$ lie in the standard $\mathbb{A}_k^{n^2}$? | |
| Dec 9, 2020 at 0:27 | comment | added | KReiser | Even if the identification is not the usual one, this shouldn't matter, right? The standard copy of $\Bbb A^{n^2}_k\subset \Bbb A^{n^2}_{\overline{k}}$ is dense because $k$ is infinite, and then the image of $D$ in the standard $\Bbb A^{n^2}_k$ is of the same dimension, so it must be dense too. So the image of $D$ in $\Bbb A^{n^2}_{\overline{k}}$ is dense, and must intersect $U$. | |
| Dec 9, 2020 at 0:16 | comment | added | darij grinberg | Just meant this should probably be said in the post :) I agree -- this argument looks fishy. | |
| Dec 8, 2020 at 23:59 | comment | added | Rita | @darijgrinberg: I'm reading the second edition (so I guess if I'm interpreting it correctly this was not corrected in the revision!). | |
| Dec 8, 2020 at 23:57 | review | First posts | |||
| Dec 9, 2020 at 2:29 | |||||
| Dec 8, 2020 at 23:56 | comment | added | darij grinberg | Note: The book has two editions. | |
| Dec 8, 2020 at 23:54 | history | asked | Rita | CC BY-SA 4.0 |