  We formulate for function fields an analog of Serre's conjecture on the
modularity of 2-dimensional irreducible mod l representations of the absolute
Galois group of Q: our analog is not restricted to 2-dimensional
represntations. While the original conjecture of Serre is wide open at the
moment, in this paper we prove the function field analog of Serre's conjecture
only assuming largeness of image of the representation and some assumptions on
the ramification of the representation (for example if the mod l representation
is unramified and has full image, l is odd and the dimension and characteristic
of the representation are coprime).
