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I am looking for a road to understanding what quasi-algebraically closed fields are with the ultimate goal of understanding the paper by Lang 1952.

My current background is the first 6 chapters from Milne's notes here. Currently I am also studying the 7th chapter from the same notes and the chapter on Brauer groups from Milne's notes on class field theory.

I am also familiar with Russian besides English. Apologizes if the question is not placed in an appropriate place, but I really seek some help here.

EDIT: At the advice given in a comment here, I deleted the post from here and moved the question to Stack Exchange, but it did not receive any answers there, so I undeleted this post.

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    $\begingroup$ This question is more appropriate in math.stackexchange but a good reference is the book by M. J. Greenberg, Forms of Higher Degree. $\endgroup$
    – Felipe Voloch
    Commented Feb 26, 2017 at 21:27
  • $\begingroup$ Thank you for the reference, but upon a google search, I did not find your title. Did you mean instead Lectures on Forms in Many Variables by Marvin Greenberg? $\endgroup$
    – user223794
    Commented Mar 12, 2017 at 17:52
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    $\begingroup$ There is some material on $C_i$ fields in general, and some results on $C_1$ fields in particular, in Fried & Jarden's Field Arithmetic (the index isn't good, but it's mostly in chapter 21, "Problems of Arithmetical Geometry", at least in the 3rd edition of 2008). Admittedly, there isn't much, but I'm not sure exactly what sort of things you're looking for. $\endgroup$
    – Gro-Tsen
    Commented Mar 12, 2017 at 18:39
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    $\begingroup$ @user223794 Yes, that's the one I mean. Must have confused it with something else. $\endgroup$
    – Felipe Voloch
    Commented Mar 12, 2017 at 22:42

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