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On Grothendieck’s conjecture of birational anabelian geometry. (English) Zbl 0814.14027

Let \(K\) and \(L\) be a number fields and \(G_ K\), \(G_ L\) be their absolute Galois groups. Then the canonical map \(\text{Hom}(K,L) \to \text{Out}(G_ K,G_ L)\) is a bijection (Neukirch, Ikeda, Iwasawa, Uchida). The author proves a generalization of this result for the function fields of one variable over a finitely generated field. This result was conjectured by Grothendieck in the frames of his anabelian geometry.

MSC:

14H05 Algebraic functions and function fields in algebraic geometry
11R32 Galois theory
14G25 Global ground fields in algebraic geometry
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