Advanced Studies in Pure Mathematics

On cuspidal sections of algebraic fundamental groups

Jakob Stix

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Abstract

Rational points in the boundary of a hyperbolic curve over a field with sufficiently nontrivial Kummer theory are the source for an abundance of sections of its fundamental group extension. We refine Nakamura's approach to these sections and obtain an anabelian theorem for hyperbolic genus 0 curves over quite general fields, for example $\mathbb{Q}^{\mathrm{ab}}$.

Article information

Source
Galois–Teichmüller Theory and Arithmetic Geometry, H. Nakamura, F. Pop, L. Schneps and A. Tamagawa, eds. (Tokyo: Mathematical Society of Japan, 2012), 519-563

Dates
Received: 12 March 2011
Revised: 24 February 2012
First available in Project Euclid: 24 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540417829

Digital Object Identifier
doi:10.2969/aspm/06310519

Mathematical Reviews number (MathSciNet)
MR3051254

Zentralblatt MATH identifier
1321.14027

Subjects
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 14G05: Rational points 12E30: Field arithmetic

Keywords
Section conjecture anabelian geometry

Citation

Stix, Jakob. On cuspidal sections of algebraic fundamental groups. Galois–Teichmüller Theory and Arithmetic Geometry, 519--563, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06310519. https://projecteuclid.org/euclid.aspm/1540417829


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