On Grothendieck's conjecture of birational anabelian geometry (Q1319114)
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scientific article; zbMATH DE number 549325
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Grothendieck's conjecture of birational anabelian geometry |
scientific article; zbMATH DE number 549325 |
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On Grothendieck's conjecture of birational anabelian geometry (English)
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20 June 1995
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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.
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absolute Galois groups
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function fields of one variable
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anabelian geometry
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