Let be the Néron model of an abelian variety over the fraction field of a discrete valuation ring . By work of Mazur and Messing, there is a functorial way to prolong the universal extension of by a vector group to a smooth and separated group scheme over , called the canonical extension of . Here we study the canonical extension when is the Jacobian of a smooth, proper and geometrically connected curve over . Assuming that admits a proper flat regular model over that has generically smooth closed fiber, our main result identifies the identity component of the canonical extension with a certain functor classifying line bundles on 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 of with the functor . As an application of our result, we prove a comparison isomorphism between two canonical integral structures on the de Rham cohomology of .
"Canonical extensions of Néron models of Jacobians." Algebra Number Theory 4 (2) 111 - 150, 2010. https://doi.org/10.2140/ant.2010.4.111