On Mordell-Weil groups of Jacobians over function fields

Douglas Ulmer

On Mordell-Weil groups of Jacobians over function fields

Number Theory 2011-02-21 v3 Algebraic Geometry

Authors: Douglas Ulmer

Abstract

We study the arithmetic of abelian varieties over $K=k(t)$ where $k$ is an arbitrary field. The main result relates Mordell-Weil groups of certain Jacobians over $K$ to homomorphisms of other Jacobians over $k$ . Our methods also yield completely explicit points on elliptic curves with unbounded rank over $\Fpbar(t)$ and a new construction of elliptic curves with moderately high rank over $\C(t)$ .

Keywords

abelian varieties hyperelliptic curves abel-jacobi theory

Cite

@article{arxiv.1002.3310,
  title  = {On Mordell-Weil groups of Jacobians over function fields},
  author = {Douglas Ulmer},
  journal= {arXiv preprint arXiv:1002.3310},
  year   = {2011}
}

Comments

v1: 25 pages; v2=v1, ignore; v3: Corrects rank formula when the covers C_d or D_d are reducible and includes other minor improvements and simplifications

On Mordell-Weil groups of Jacobians over function fields

Abstract

Keywords

Cite

Comments

Related papers