The Profinite Grothendieck Conjecture for Closed Hyperbolic Curves over Number Fields
Vol. 3 (1996), No. 3, Page 571--627.
Mochizuki, Shinichi
The Profinite Grothendieck Conjecture for Closed Hyperbolic Curves over Number Fields
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Abstract:
In 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.
Mathematics Subject Classification (1991): Primary 11G30; Secondary 14H25, 14H30, 11G20, 11G80
Mathematical Reviews Number: MR1432110
Received: 1995-12-14
