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On copies of the absolute Galois group in $ \operatorname{Out}F_2$


Author: Robert A. Kucharczyk
Journal: Proc. Amer. Math. Soc. 144 (2016), 2351-2359
MSC (2010): Primary 11G05, 11G32, 11R32, 14G25
DOI: https://doi.org/10.1090/proc/12917
Published electronically: October 20, 2015
MathSciNet review: 3477052
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Abstract: In this article we consider outer Galois actions on a free profinite group of rank two, induced by the étale fundamental group of a projective line minus three points or of a pointed elliptic curve over a number field. Under mild technical assumptions their respective images uniquely determine the curves and the number fields.


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Additional Information

Robert A. Kucharczyk
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany—and—Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Email: robert.kucharczyk@math.ethz.ch

DOI: https://doi.org/10.1090/proc/12917
Keywords: Anabelian geometry, elliptic curves, \'etale fundamental groups, Galois actions
Received by editor(s): November 20, 2014
Received by editor(s) in revised form: July 18, 2015
Published electronically: October 20, 2015
Additional Notes: This research was supported by the European Research Council
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2015 American Mathematical Society