On the birational section conjecture over finitely generated fields

Saïdi, Mohamed; Tyler, Michael

doi:10.2140/ant.2021.15.435

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On the birational section conjecture over finitely generated fields

Mohamed Saïdi and Michael Tyler

Vol. 15 (2021), No. 2, 435–460

DOI: 10.2140/ant.2021.15.435

Abstract

We investigate the birational section conjecture for curves over function fields of characteristic zero and prove that the conjecture holds over finitely generated fields over $ℚ$ if it holds over number fields.

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Keywords

birational anabelian section conjecture, curves over finitely generated fields

Mathematical Subject Classification 2010

Primary: 11G30

Milestones

Received: 22 August 2019

Revised: 4 June 2020

Accepted: 5 July 2020

Published: 7 April 2021

Authors

Mohamed Saïdi
School of Engineering, Mathematics and Physical Sciences University of Exeter Exeter United Kingdom

Michael Tyler
School of Engineering, Mathematics and Physical Sciences University of Exeter Exeter United Kingdom

Vol. 15, No. 2, 2021