NAG

Abstract

We compute, jointly with P. Deligne, the number of equivalence classes of irreducible rank n ell-adic local systems on the geometric X-S, namely n-dimensional ell-adic representations of pi_1(geometrix(X-S)), invariant under the Frobenius, whose local monodromy at each point of S is a single Jordan block of rank n. Here X is a smooth projective absolutely irreducible curve over the finite field of cardinality q, S a finite set of closed points of X of cardinality N>1, ell a prime with (ell,q)=1, and n>1 an integer.