2022-01-25T05:04:23Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000403142021-03-01T21:01:59ZThe Profinite Grothendieck Conjecture for Closed Hyperbolic Curves over Number FieldsMochizuki, Shinichi138911415application/pdfIn this paper, we extend the results of [Tama] on the Grothendieck Conjecture for affine hyperbolic curves over finite fields to obtain a Grothendieck Conjecture-type result for singular, proper, stable log-curves over finite fields. Using this result, we derive a strong Grothendieck Conjecture-type result for smooth, proper hyperbolic curves over number fields, and a weak Grothendieck Conjecture-type result for smooth, proper, hyperbolic curves over local fields with ordinary reduction.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo1996application/pdfJournal of mathematical sciences, the University of Tokyo33571627AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40314/files/jms030305.pdfeng