Publications of the Research Institute for Mathematical Sciences
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Published online: 2010-11-18
Existence of Nongeometric Pro-p Galois Sections of Hyperbolic CurvesYuichiro Hoshi (1) Kyoto University, Japan
We construct a nongeometric pro-p Galois section of a proper hyperbolic curve over a number field, as well as over a p-adic local field. This yields a negative answer to the pro-p 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-p Galois sections.
Keywords: pro-p Galois section, hyperbolic curve, Section Conjecture, number field, p-adic local field
Hoshi Yuichiro: Existence of Nongeometric Pro-p Galois Sections of Hyperbolic Curves. Publ. Res. Inst. Math. Sci. 46 (2010), 829-848. doi: 10.2977/PRIMS/27