TY - JOUR
T1 - A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary characteristic
AU - Lüdtke, Martin
N1 - Publisher Copyright:
© 2018, Hebrew University of Jerusalem.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85051238716&partnerID=8YFLogxK
UR - https://arxiv.org/pdf/1706.01713
U2 - 10.1007/s11856-018-1757-2
DO - 10.1007/s11856-018-1757-2
M3 - Article
AN - SCOPUS:85051238716
SN - 0021-2172
VL - 227
SP - 987
EP - 1011
JO - Israel journal of mathematics
JF - Israel journal of mathematics
IS - 2
ER -