Abstract
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.
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