Mathematics – Algebraic Geometry
Scientific paper
2009-09-09
Mathematics
Algebraic Geometry
To appear in Algebra & Number Theory
Scientific paper
Let A be the N\'eron model of an abelian variety A_K over the fraction field K of a discrete valuation ring R. Due to work of Mazur-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. In this paper, 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^{\natural,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 N\'eron 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.
No associations
LandOfFree
Canonical extensions of Néron models of Jacobians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Canonical extensions of Néron models of Jacobians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical extensions of Néron models of Jacobians will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-131083