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Abstract

Let k be the algebraic closure of the field with q elements. We build upon recent work of Ulmer and Berger to give examples of elliptic curves and higher dimensional abelian varieties over the field K = k(t) with the property that their ranks become arbitrarily large when dth roots of the variable t are adjoined to K for d varying across the integers relatively prime to q. We also give a first example of an elliptic curve whose rank under such extensions grows linearly in d, for those d prime to q.

Details

Title
Mordell -Weil groups of large rank in towers
Author
Occhipinti, Thomas
Year
2010
Publisher
ProQuest Dissertations & Theses
ISBN
978-1-109-73620-5
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
304677857
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.