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.
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