## Canonical Integral Structures on the de Rham Cohomology of Curves

For a smooth and proper curve X_{K} 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}/K) with a
**canonical integral structure**:
i.e. an R-lattice which is functorial in finite (generically etale) K-morphisms of X_{K} and which is
preserved by the cup-product auto-duality on H^{1}_{dR}(X_{K}/K).
Our construction of this lattice uses
a certain class of normal proper models
of X_{K} 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_{K}
and that the index for this inclusion of lattices is a numerical invariant of X_{K}
(we call it the de Rham conductor).
Using work of Bloch and Liu-Saito, we prove that the de Rham conductor of X_{K}
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_{K} is affected by finite extension of scalars.

This paper strengthens and extends the work of Chapter 2
of my PhD thesis.

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