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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Galois rigidity of pro-$l$ pure braid groups of algebraic curves
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by Hiroaki Nakamura and Naotake Takao PDF
Trans. Amer. Math. Soc. 350 (1998), 1079-1102 Request permission

Abstract:

In this paper, Grothendieck’s anabelian conjecture on the pro-$l$ fundamental groups of configuration spaces of hyperbolic curves is reduced to the conjecture on those of single hyperbolic curves. This is done by estimating effectively the Galois equivariant automorphism group of the pro-$l$ braid group on the curve. The process of the proof involves the complete determination of the groups of graded automorphisms of the graded Lie algebras associated to the weight filtration of the braid groups on Riemann surfaces.
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Additional Information
  • Hiroaki Nakamura
  • Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
  • Email: h-naka@ms.u-tokyo.ac.jp
  • Naotake Takao
  • Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Kyoto 606-01, Japan
  • Email: takao@kurims.kyoto-u.ac.jp
  • Received by editor(s): September 10, 1995
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 1079-1102
  • MSC (1991): Primary 14E20; Secondary 20F34, 20F36
  • DOI: https://doi.org/10.1090/S0002-9947-98-02038-8
  • MathSciNet review: 1443885