On torsors under elliptic curves and Serre's pro-algebraic structures

Details On torsors under elliptic curves and Serre's pro-algebraic structures On torsors under elliptic curves and Serre's pro-algebraic structures

2012-04-12

arxiv.org/abs/1204.2805v1

Mathematics

Algebraic Geometry

This paper arises from the confluence and the comparison of the results contained in the preprints arXiv:1106.1540v2 and arXiv

Scientific paper

Let $K$ be a local field with algebraically closed residue field and $X_K$ a torsor under an elliptic curve $J_K$ over $K$. Let $X$ be a proper minimal regular model of $X_K$ over the ring of integers of $K$ and $J$ the identity component of the N\'eron model of $J_K$. We study the canonical morphism $q\colon \mathrm{Pic}^{0}_{X/S}\to J$ which extends the biduality isomorphism on generic fibres. We show that $q$ is pro-algebraic in nature with a construction that recalls Serre's work on local class field theory. Furthermore we interpret our results in relation to Shafarevich's duality theory for torsors under abelian varieties.

Affiliated with

Also associated with

No associations

Rating

On torsors under elliptic curves and Serre's pro-algebraic structures 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 On torsors under elliptic curves and Serre's pro-algebraic structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On torsors under elliptic curves and Serre's pro-algebraic structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-313250