Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 203 (2011), 47-100.
Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero
Let be a prime number. In this paper, we prove that the isomorphism class of an -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- outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.
Nagoya Math. J. Volume 203 (2011), 47-100.
First available in Project Euclid: 18 August 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 14H10: Families, moduli (algebraic)
Hoshi, Yuichiro. Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero. Nagoya Math. J. 203 (2011), 47--100. doi:10.1215/00277630-1331863. https://projecteuclid.org/euclid.nmj/1313682312