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.
Reviewer: A.N.Parshin (Moskva)
MSC:
14H05 | Algebraic functions and function fields in algebraic geometry |
11R32 | Galois theory |
14G25 | Global ground fields in algebraic geometry |