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SUMMARY:On the combinatorial cuspidalizations and the faithfulness of the 
 outer Galois representations of hyperbolic curves - Hoshi\, Y (Kyoto)
DTSTART:20090827T130000Z
DTEND:20090827T140000Z
UID:TALK19587@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk\, I discuss the combinatorial anabelian geometry 
 for nodally nondegenerate outer representations on the fundamental groups 
 of hyperbolic curves. I plan to explain a result of a combinatorial\nversi
 on of the Grothendieck conjecture for nodally nondegenerate outer represen
 tations obtained in the joint work with Shinichi Mochizuki. As an applicat
 ion\, we prove the injectivity portion of the combinatorial cuspidalizatio
 n. We also generalize\, by means of this injectivity result\, the faithful
 ness proven by Makoto Matsumoto of the outer representation of the absolut
 e Galois group on the profinite fundamental group of an\naffine hyperbolic
  curve over a certain field (e.g. number or p-adic local field) to the cas
 e where the given hyperbolic curve is proper.\n
LOCATION:Seminar Room 1\, Newton Institute
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