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Abstract

Let A be the Néron model of an abelian variety A K over the fraction field K of a discrete valuation ring R. By work of Mazur and Messing, there is a functorial way to prolong the universal extension of A K by a vector group to a smooth and separated group scheme over R, called the canonical extension of A. Here we study the canonical extension when A K = J K is the Jacobian of a smooth, proper and geometrically connected curve X K over K. Assuming that X K admits a proper flat regular model X over R that has generically smooth closed fiber, our main result identifies the identity component of the canonical extension with a certain functor Pic ,0 X/R classifying line bundles on X that have partial degree zero on all components of geometric fibers and are equipped with a regular connection. This result is a natural extension of a theorem of Raynaud, which identifies the identity component of the Néron model J of J K with the functor Pic 0 X/R. As an application of our result, we prove a comparison isomorphism between two canonical integral structures on the de Rham cohomology of X K .