I am seeking references to any proofs of Shafarevich's theorem about solvable groups being Galois groups.
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2$\begingroup$ There is an old book by Shatz called "Pro-Finite Groups, Arithmetic, and Geometry" that has a proof. I like the proof, but that may be a chocolate/vanilla thing. $\endgroup$– mehCommented Aug 7, 2018 at 18:24
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$\begingroup$ Nice..i adore chocolate..😍 $\endgroup$– Mohammad RadiCommented Aug 7, 2018 at 18:30
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2$\begingroup$ @aginensky Are you mistaking the theorem asked about in the question with Shafarevich's solution of the class tower problem? The table of contents in the google preview of Shatz's book doesn't list anything related to the inverse Galois problem for solvable groups. Besides that, as far as I know the much more recent paper given in mathphysicist's answer is the first correct proof of Shafarevich's theorem. $\endgroup$– Peter MuellerCommented Aug 7, 2018 at 21:48
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5$\begingroup$ A proof is in Chapter IX, Section 6 of Neukirch, Schmidt, and Wignberg's "Cohomology of Number Fields". $\endgroup$– KConradCommented Aug 8, 2018 at 0:24
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$\begingroup$ I second @aginensky's recommendation for Shatz's lovely book, even if it doesn't contain a proof of the theorem (I don't have it to hand, so can't check). :-) $\endgroup$– LSpiceCommented Aug 8, 2018 at 2:34
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1 Answer
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Also, the paper Safarevic's Theorem on Solvable Groups as Galois Groups (freely available on arXiv) gives the proof.
answered Aug 7, 2018 at 19:17
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$\begingroup$ My problem is that i cant understand that proof because i need to know what galois theory i need to understand it $\endgroup$ Commented Aug 7, 2018 at 19:20