2,080 research outputs found
On Mordell-Weil groups of Jacobians over function fields
We study the arithmetic of abelian varieties over where is an
arbitrary field. The main result relates Mordell-Weil groups of certain
Jacobians over to homomorphisms of other Jacobians over . 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).Comment: 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
simplification
- …