On the birational section conjecture with local conditions

Details On the birational section conjecture with local conditions On the birational section conjecture with local conditions

2012-03-14

arxiv.org/abs/1203.3236v2

Mathematics

Algebraic Geometry

Added missing assumption in Theorem D

Scientific paper

We prove that birational Galois sections for smooth curves over Q all have image in a decomposition group of a Q-rational point if and only if certain associated 2-dimensional Galois representations are either reducible or form a compatible $\ell$-adic system. This provides a birational variant endowed with an additional group theoretic condition of Grothendieck's section conjecture in anabelian geometry. We find here the first GL_2-type argument in anabelian geometry which usually only depends on prosolvable quotients. As an aside we also obtain a strong approximation result for rational points on hyperbolic curves over Q or imaginary quadratic fields.

Affiliated with

Also associated with

No associations

Rating

On the birational section conjecture with local conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the birational section conjecture with local conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the birational section conjecture with local conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-30060