Let X1β be a projective, smooth and geometrically connected curve over
Fqβ with q=pn elements where p is a prime number, and let
X be its base change to an algebraic closure of Fqβ. We give a
formula for the number of irreducible β-adic local systems (βξ =p)
with a fixed rank over X fixed by the Frobenius endomorphism. We prove that
this number behaves like a Lefschetz fixed point formula for a variety over
Fqβ, which generalises a result of Drinfeld in rank 2 and proves a
conjecture of Deligne. To do this, we pass to the automorphic side by Langlands
correspondence, then use Arthur's non-invariant trace formula and link this
number to the number of Fqβ-points of the moduli space of stable
Higgs bundles.Comment: In French; improved a littl