Timeline for What is the general statement of Hilbert 90?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Oct 30, 2011 at 23:25 | comment | added | Moosbrugger | One general form is that $GL_n$-torsors in the fppf (or a fortiori etale) topology coincide with Zariski $GL_n$-torsors (alias: rank $n$ vector bundles). Your first statement follows, since the left hand side computes isomorphism classes of etale $GL_n$-torsors on $\Spec(K)$, which then coincides with isomorphism classes of rank $n$ vector bundles on $\Spec(K)$, which is obviously just the one. Your second statement (which is a little imprecise, but presumably your $H^1$ is etale) is this for $n=1$. | |
| Oct 30, 2011 at 23:20 | vote | accept | Makhalan Duff | ||
| Oct 30, 2011 at 23:06 | answer | added | Pavel Safronov | timeline score: 5 | |
| Oct 30, 2011 at 22:56 | history | asked | Makhalan Duff | CC BY-SA 3.0 |