Fibres multiples des surfaces

Abstract

We show that Lang's hyperbolic and function version conjectures hold for surfaces $S$ of general type having a fibration of general type onto a curve $C$. The notion of multiplicity used is natural, but not classical, which leds to orbifold versions of Mordell's conjectures not reducible by ramified covering tricks to the already solved cases. These are solved here in the two above case (hyperbolic and function field cases). But the arithmetic case (which follows from the abc conjecture) is left open. We also give an example of a simply connected surface of general type having a fibration of general type on $\Bbb P^1$, showing that the non-classical notion of multiplicity used does not impose conditions on the fundamental group.