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Mar 26, 2018 at 15:46 comment added Max CYLin @JasonStarr Thanks for your comments! Any suggestion for second question ?
Mar 22, 2018 at 9:05 comment added Jason Starr Effectively you can choose $V_1$ to be a particular (absolutely / geometrically) irreducible variety $W$. This is equivalent to running through the proof with the field $K$ replaced by the regular extension field $K(W)$. For your second question, I completely agree that this is not obvious. The construction that I know for $K_1$ uses Zorn's lemma for the partially ordered set of chains of regular field extensions, but they need not be extensions of the form $\prod_{\alpha<\beta} F_\alpha \to \prod_{\alpha \leq \beta} F_\alpha$.
Mar 22, 2018 at 8:28 history edited Max CYLin CC BY-SA 3.0
edited title
S Mar 20, 2018 at 15:30 history suggested Pooter CC BY-SA 3.0
removed a weird line break
Mar 20, 2018 at 14:11 review Suggested edits
S Mar 20, 2018 at 15:30
Mar 19, 2018 at 17:10 history asked Max CYLin CC BY-SA 3.0