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 extensionof . 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 .
Keywords
canonical extensions, Néron models, Jacobians, relative
Picard functor, group schemes, Grothendieck's pairing,
Grothendieck duality, integral structure, de Rham
cohomology, abelian variety, rigidified extensions