On the Hom-form of Grothendieck’s birational anabelian conjecture in positive characteristic

Saïdi, Mohamed; Tamagawa, Akio

doi:10.2140/ant.2011.5.131

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On the Hom-form of Grothendieck's birational anabelian conjecture in positive characteristic

Mohamed Saïdi and Akio Tamagawa

Vol. 5 (2011), No. 2, 131–184

DOI: 10.2140/ant.2011.5.131

Abstract

We prove that a certain class of open homomorphisms between Galois groups of function fields of curves over finite fields arises from embeddings between the function fields.

Keywords

Grothendieck's birational anabelian conjecture, homomorphisms between Galois groups

Mathematical Subject Classification 2010

Primary: 14G15

Secondary: 14H25, 14H30, 11G20

Milestones

Received: 2 December 2009

Revised: 1 May 2010

Accepted: 6 June 2010

Published: 27 August 2011

Authors

Mohamed Saïdi
University of Exeter School of Engineering, Computing and Mathematics Exeter EX44QF United Kingdom

Akio Tamagawa
Kyoto University Research Institute for Mathematical Sciences Kyoto 606-8502 Japan

Vol. 5, No. 2, 2011