Timeline for Evidence for $Q^{\operatorname{solv}}$ being pseudo-algebraically-closed
Current License: CC BY-SA 2.5
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| Nov 22, 2009 at 22:21 | comment | added | Pete L. Clark | (At least I think...): Yes. it follows using (i) that every finite extension of a local field is solvable, and (ii) the observation that local extensions of the form X^n - a can be approximated by global extensions of that form (Krasner's Lemma). The assumption about Brauer-Manin would give you that once you've made a solvable extension to get points everywhere locally, then either you have a global point or you have a Brauer obstruction. Are you suggesting that you could then kill the Brauer obstruction by making a further solvable extension? That's interesting... | |
| Nov 22, 2009 at 22:13 | history | answered | JSE | CC BY-SA 2.5 |