Galoismoduln mit Hasse-Prinzip [Galois modules with Hasse principle]

URN to cite this document:: urn:nbn:de:bvb:355-epub-266918
DOI to cite this document:: 10.5283/epub.26691

Jannsen, Uwe

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Date of publication of this fulltext: 14 Nov 2012 10:31

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Abstract

Let k be an algebraic number field and A a finite, irreducible Gk-module. We show that the localization mapping H1(k,A)→∏pH1(kp,A) is injective (or that for imbedding problems with such a kernel A the full local-global principle holds), if the trivializing extension k(A)/k is p-solvable (p is the prime number with pA=0), and that for nonsolvable k(A)/k this is in general false (counterexample ...