Existence of Nongeometric Pro- Galois Sections of Hyperbolic Curves

  • Yuichiro Hoshi

    Kyoto University, Japan

Abstract

We construct a nongeometric pro- Galois section of a proper hyperbolic curve over a number field, as well as over a -adic local field. This yields a negative answer to the pro- version of the anabelian Grothendieck Section Conjecture. We also observe that there exists a proper hyperbolic curve over a number field which admits infinitely many conjugacy classes of pro- Galois sections.

Cite this article

Yuichiro Hoshi, Existence of Nongeometric Pro- Galois Sections of Hyperbolic Curves. Publ. Res. Inst. Math. Sci. 46 (2010), no. 4, pp. 829–848

DOI 10.2977/PRIMS/27