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Transactions of the American Mathematical Society

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Galois rigidity of pro-$l$ pure braid groups
of algebraic curves

Authors: Hiroaki Nakamura and Naotake Takao
Journal: Trans. Amer. Math. Soc. 350 (1998), 1079-1102
MSC (1991): Primary 14E20; Secondary 20F34, 20F36
MathSciNet review: 1443885
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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

Naotake Takao
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Kyoto 606-01, Japan

Keywords: Galois representation, anabelian geometry, braid group
Received by editor(s): September 10, 1995
Article copyright: © Copyright 1998 American Mathematical Society