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

Canonical integral structures on the de Rham cohomology of curves