Existence of nongeometric pro-p Galois sections of hyperbolic curves

Mardi 2 février 2010 16:00-17:00 - Hoshi Yuichiro - RIMS (Japon)

Résumé : In this talk, we construct a nongeometric pro-p Galois section of a hyperbolic curve over a number field, as well as over a p-adic local field. Moreover, we observe that there exists a proper hyperbolic curve over a number field which admits infinitely many conjugacy classes of pro-p Galois sections. The existence of such pro-p Galois sections yields a negative answer to the pro-p section conjecture --- i.e., the pro-p version of Grothendieck’s section conjecture --- over number fields, as well as over p-adic local fields.

Lieu : bât. 425 - 113-115

Existence of nongeometric pro-p Galois sections of hyperbolic curves  Version PDF
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