We describe a new invariant for the action of the absolute Galois groups on the set of Grothendieck dessins. It uses the fact that the automorphism groups of regular dessins are isomorphic to automorphism groups of the corresponding Riemman surfaces and define linear represenatations of the space of holomorphic differentials. The characters of these representations give more precise information about the action of the Galois group than all previously known invariants, as it is shown by a series of examples. These examples have their own interest because the Galois action on them is described only using properties of the fixed points in the canonical model, without the explicit knowledge of equations.
@article{urn:eudml:doc:44370,
title = {Characteres and Galois invariants of regular dessins.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {13},
year = {2000},
pages = {49-81},
zbl = {1053.14021},
mrnumber = {MR1794903},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44370}
}
Streit, Manfred; Wolfart, Jürgen. Characteres and Galois invariants of regular dessins.. Revista Matemática de la Universidad Complutense de Madrid, Tome 13 (2000) pp. 49-81. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44370/