  Green's Conjecture predicts than one can read off special linear series on an
algebraic curve, by looking at the syzygies of its canonical embedding. We
extend Voisin's results on syzygies of K3 sections, to the case of K3 surfaces
with arbitrary Picard lattice. This, coupled with results of Voisin and
Hirschowitz-Ramanan, provides a complete solution to Green's Conjecture for
smooth curves on arbitrary K3 surfaces.
