Full paper in PDF:
$%M. Streit and J. Wolfart, Characters and Galois invariants of regular dessins, Rev. Mat. Complut. 13 (2000), no. 1, 4981.%$

Characters and Galois Invariants of Regular Dessins
Manfred STREIT and Jürgen WOLFART
Mathematisches Seminar der J. W. Goethe-Universität
Robert-Mayer-Str. 6–10
D-60054 Frankfurt a.M. — Germany

Received: November 26, 1998
Revised: June 17, 1999

ABSTRACT

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 Riemann surfaces and define linear representations on 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.

1991 Mathematics Subject Classification: 14H30, 20H10, 30F10, 11F70, 11F80.