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On Mordell–Weil groups of Jacobians over function fields

Published online by Cambridge University Press:  15 May 2012

Douglas Ulmer*
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA(ulmer@math.gatech.edu)

Abstract

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 and a new construction of elliptic curves with moderately high rank over .

Type
Research Article
Copyright
Copyright © Cambridge University Press 2013

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