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.
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.
@article{AFST_2008_6_17_4_765_0,
author = {Marin, Ivan},
title = {Characters of the {Grothendieck-Teichm\"uller} group through rigidity of the {Burau} representation},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {765--780},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 17},
number = {4},
year = {2008},
doi = {10.5802/afst.1202},
zbl = {1160.14009},
mrnumber = {2499855},
language = {en},
url = {http://www.numdam.org/articles/10.5802/afst.1202/}
}
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 PY - 2008 SP - 765 EP - 780 VL - 17 IS - 4 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1202/ DO - 10.5802/afst.1202 LA - en ID - AFST_2008_6_17_4_765_0 ER -
%0 Journal Article %A Marin, Ivan %T Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2008 %P 765-780 %V 17 %N 4 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1202/ %R 10.5802/afst.1202 %G en %F AFST_2008_6_17_4_765_0
Marin, Ivan. Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 4, pp. 765-780. doi : 10.5802/afst.1202. http://www.numdam.org/articles/10.5802/afst.1202/
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