Timeline for First Galois cohomology of Weil restriction of $\mathbb{G}_m$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2016 at 3:43 | comment | added | nfdc23 | @WillSawin: Thanks for noting my oversight when reading the original question (and for noting why it ultimately addresses the question posed as a special case). | |
| Feb 3, 2016 at 3:40 | history | edited | nfdc23 | CC BY-SA 3.0 |
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| Feb 3, 2016 at 3:32 | comment | added | Will Sawin | It's important to note that Sasha asked for $\operatorname{Gal}(L/K)$-cohomology and not $\operatorname{Gal}(K)$ cohomology. In particular, this is the source of the assumption that $L/K$ be Galois! To check that your answer applies, we apply a spectral sequence to equation the $\operatorname{Gal}(K)$-cohomology of a group scheme to the $\operatorname{Gal}(L/K)$ cohomology of its $\operatorname{Gal}(L)$-cohomology, then observe that its $\operatorname{Gal}(L)$-cohomology is equal to its $L$-points in degree $0$ (obvious) and vanishes in higher degree (Hilbert 90). | |
| S Feb 3, 2016 at 2:24 | history | answered | nfdc23 | CC BY-SA 3.0 | |
| S Feb 3, 2016 at 2:24 | history | made wiki | Post Made Community Wiki by nfdc23 |