  For a smooth and proper curve X over the fraction field K of a discrete
valuation ring R, we explain (under very mild hypotheses) how to equip the de
Rham cohomology H^1_{dR}(X/K) with a canonical integral structure: i.e. an
R-lattice which is functorial in finite (generically etale) K-morphisms of X
and which is preserved by the cup-product auto-duality on H^1_{dR}(X/K). Our
construction of this lattice uses a certain class of normal proper models of X
and relative dualizing sheaves. We show that our lattice naturally contains the
lattice furnished by the (truncated) de Rham complex of a regular proper
R-model of X and that the index for this inclusion of lattices is a numerical
invariant of X (we call it the de Rham conductor). Using work of Bloch and
Liu-Saito, we prove that the de Rham conductor of X is bounded above by the
Artin conductor, and bounded below by the Efficient conductor. We then study
how the position of our canonical lattice inside the de Rham cohomology of X is
affected by finite extension of scalars.
