Timeline for Existence of reduced norms for CSAs using fpqc descent
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2022 at 16:14 | vote | accept | Gabriel | ||
| Jan 31, 2022 at 14:53 | answer | added | Uriya First | timeline score: 2 | |
| Jan 31, 2022 at 14:53 | comment | added | Uriya First | @Gabriel Very well. | |
| Jan 30, 2022 at 8:52 | comment | added | Gabriel | @UriyaFirst This solves my question. Thank you. If you would like to turn this into an answer, I'll gladly accept it. | |
| Jan 29, 2022 at 20:09 | comment | added | Uriya First | You can define the reduced norm using fpqc descent. Have a look at chapter III, section 1.2 in Knus' "Quadratic and Hermitian Forms over Rings", for instance. | |
| Jan 29, 2022 at 16:48 | comment | added | Gabriel | @PiotrAchinger precisely! The finiteness is very simple (an isomorphism $A_{\bar{k})\cong M_n(\bar{k})$ involves only a finite amount of data, so we can find a finite extension which does the job). The hard part is proving the existence of a separable splitting field. | |
| Jan 29, 2022 at 16:41 | comment | added | Piotr Achinger | @მამუკაჯიბლაძე The way I understood the question, it's about the difference between separable and algebraic closure, not about finiteness of the splitting field extension. | |
| Jan 29, 2022 at 13:59 | comment | added | მამუკა ჯიბლაძე | A finite index subgroup of $\operatorname{Gal}(\bar k/k)$ fixes $A_{\bar k}$, what else can be said? | |
| Jan 29, 2022 at 13:39 | history | asked | Gabriel | CC BY-SA 4.0 |