Publications of the Research Institute for Mathematical Sciences


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Volume 46, Issue 4, 2010, pp. 829–848
DOI: 10.2977/PRIMS/27

Published online: 2010-11-18

Existence of Nongeometric Pro-p Galois Sections of Hyperbolic Curves

Yuichiro Hoshi[1]

(1) Kyoto University, Japan

We construct a nongeometric pro-p Galois section of a proper hyperbolic curve over a number fi eld, as well as over a p-adic local fi eld. 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 fi eld which admits in finitely 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