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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 $H_{\mathrm{dR}}^1(X_K/K)$ with a : an $R$-lattice which is functorial in finite (generically étale) $K$-morphisms of $X_K$ and which is preserved by the cup-product auto-duality on $H_{\mathrm{dR}}^1(X_K/K)$. 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...