JournalsprimsVol. 46, No. 4pp. 829–848

Existence of Nongeometric Pro-<i>p</i> Galois Sections of Hyperbolic Curves

  • Yuichiro Hoshi

    Kyoto University, Japan
Existence of Nongeometric Pro-<i>p</i> Galois Sections of Hyperbolic Curves cover
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Abstract

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.

Cite this article

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

DOI 10.2977/PRIMS/27