## 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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