On Mordell-Weil groups of Jacobians over function fields

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17 Scopus citations

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 p(t) and a new construction of elliptic curves with moderately high rank over ℂ(t).

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalJournal of the Institute of Mathematics of Jussieu
Volume12
Issue number1
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

Keywords

  • Jacobian
  • Mordell{Weil group
  • abelian variety
  • function field
  • rank

ASJC Scopus subject areas

  • Mathematics(all)

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