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ON THE NILPOTENT SECTION CONJECTURE FOR FINITE GROUP ACTIONS ON CURVES

Part of:Algebraic groupsCurves

Published online by Cambridge University Press:  13 December 2013

Ambrus Pál
Ambrus Pál*
Affiliation:
Department of Mathematics, 180 Queen’s Gate, Imperial College, London, SW7 2AZ,U.K. email a.pal@imperial.ac.uk

Abstract

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We give a new, geometric proof of the section conjecture for fixed points of finite group actions on projective curves of positive genus defined over the field of complex numbers, as well as its natural nilpotent analogue. As a part of our investigations we give an explicit description of the abelianised section map for groups of prime order in this setting. We also show a version of the $2$-nilpotent section conjecture.

MSC classification

Secondary:14H30: Coverings, fundamental group14L30: Group actions on varieties or schemes (quotients)

Information

Type
Research Article
Information
Mathematika , Volume 60 , Issue 1 , January 2014, pp. 183 - 200
Copyright
Copyright © University College London 2013 

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