Galois-theoretic Characterization of Isomorphism Classes of Monodromically Full Hyperbolic Curves of Genus Zero

@inproceedings{Hoshi2009GaloistheoreticCO,
title={Galois-theoretic Characterization of Isomorphism Classes of Monodromically Full Hyperbolic Curves of Genus Zero},
author={Y. Hoshi},
year={2009}
}

Let l be a prime number. In the present paper, we prove that the isomorphism class of an l-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-l outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to S. Mochizuki which asserts that the isomorphism class of an elliptic curve which does not… CONTINUE READING