Timeline for Existence of lift of (local) Artin map
Current License: CC BY-SA 4.0
4 events
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| Aug 29, 2022 at 20:38 | comment | added | Wojowu | You can cover the case of all primes using some finer versions of Artin-Schreier theorem, see e.g. Theorem 3.1 here. If $G_K$ has an element of order $2$ (or any other finite order other than $1$), then its fixed field would satisfy the conditions of the theorem, implying that sums of squares in $K$ don't vanish. But this doesn't hold for any local field, since some negative integers will be squares. | |
| Aug 29, 2022 at 19:32 | comment | added | curious math guy | thanks for the question and the answer! :) | |
| Aug 29, 2022 at 19:30 | vote | accept | curious math guy | ||
| Aug 29, 2022 at 19:24 | history | answered | David Loeffler | CC BY-SA 4.0 |