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user 6074
4
votes
Accepted
Galois cohomology of separable closure
Yes, they are known: They vanish in degrees $i>0$, and for $i=0$ one gets the completed perfection of $K$.
Indeed, let $K'$ be the completed perfection of $K$. Then $G_K=G_{K'}$ as both perfection and …
- 21.3k
12
votes
Accepted
Does $0\to I\to\mathrm{Gal}_K\to\mathrm{Gal}_k\to 0$ always split?
Good question! Let me try to guess what Gabber had in mind there. (Note that he only says "known" (to him), not "well-known"...)
The claim is that the extension splits. Note that to prove this, we are …
- 21.3k