A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary characteristic

Martin Lüdtke*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

The aim of Bogomolov's programme is to prove birational anabelian conjecturesfor function fields K|k of varieties of dimension ≥2 over algebraicallyclosed fields. The present article is concerned with the 1-dimensional case.While it is impossible to recover K|k from its absolute Galois group alone,we prove that it can be recovered from the pair (Aut(K|k),Aut(K|K)), consisting ofthe absolute Galois group of K and the larger group of field automorphisms fixing only the base field.
Original languageEnglish
Pages (from-to)987-1011
Number of pages25
JournalIsrael journal of mathematics
Volume227
Issue number2
DOIs
Publication statusPublished - 1-Aug-2018

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