On cuspidal sections of algebraic fundamental groups

Details On cuspidal sections of algebraic fundamental groups On cuspidal sections of algebraic fundamental groups

2008-08-29

arxiv.org/abs/0809.0017v1

Mathematics

Algebraic Geometry

Scientific paper

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 the fundamental group exact sequence. We follow and refine Nakamura's approach towards these boundary sections. For example, we obtain a weak anabelian theorem for hyperbolic genus 0 curves over quite general fields including for example the maximal abelian extension of the rational numbers.

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