Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation

Ivan Marin[1]

  • [1] Institut de Mathématiques de Jussieu, Université Paris 7, 175 rue du Chevaleret, F-75013 Paris

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 4, page 765-780
  • ISSN: 0240-2963

Abstract

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We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmüller groups.

How to cite

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Marin, Ivan. "Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation." Annales de la faculté des sciences de Toulouse Mathématiques 17.4 (2008): 765-780. <http://eudml.org/doc/10105>.

@article{Marin2008,
abstract = {We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmüller groups.},
affiliation = {Institut de Mathématiques de Jussieu, Université Paris 7, 175 rue du Chevaleret, F-75013 Paris},
author = {Marin, Ivan},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {6},
number = {4},
pages = {765-780},
publisher = {Université Paul Sabatier, Toulouse},
title = {Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation},
url = {http://eudml.org/doc/10105},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Marin, Ivan
TI - Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 4
SP - 765
EP - 780
AB - We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmüller groups.
LA - eng
UR - http://eudml.org/doc/10105
ER -

References

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  5. Ichimura (H.), Sakaguchi (K.).— The non-vanishing of a certain Kummer character χ m (after C. Soulé), and some related topics, in Galois representations and arithmetic algebraic geometry, Proc. Symp., Kyoto 1985 and Tokyo 1986, Adv. Stud. Pure Math. 12, p. 53-64 (1987). Zbl0647.12007MR948236
  6. Katz (N.).— Rigid local systems, Annals of Math. Studies 139, Princeton University Press (1996). Zbl0864.14013MR1366651
  7. Marin (I.).— Caractères de rigidité du groupe de Grothendieck-Teichmüller, Compos. Math. 142, p. 657-678 (2006). Zbl1133.14027MR2231196
  8. Nakamura (H.).— Limits of Galois representations in fundamental groups along maximal degeneration of marked curves I, Amer. J. Math 121, p. 315-358 (1999). Zbl1006.12001MR1680325
  9. Nakamura (H.), Schneps (L.).— On a subgroup of the Grothendieck-Teichmüller group acting on the tower of profinite Teichmüller modular groups, Invent. Math. 141, p. 503-560 (2000). Zbl1077.14030MR1779619

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