Champs de Hurwitz

Abstract

We give a thorough study of Hurwitz stacks both in Galois and non galois case. The construction is applied to revisit somme classical examples, the stack of stable curves equipped with a level structure, and the stacks of tamely ramified cyclic covers. We exhibit some tautological cohomology classes, and give some universal relations between them. Applications are given to Cornalba-Harris type relations, and to some Hurwitz-Hodge integrals.