Persistent Link:
http://hdl.handle.net/10150/194213
Title:
Mordell-Weil Groups of Large Rank in Towers
Author:
Occhipinti, Thomas
Issue Date:
2010
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
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.
Type:
text; Electronic Dissertation
Keywords:
Function Fields; Number Theory; Ranks; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Ulmer, Douglas
Committee Chair:
Ulmer, Douglas

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleMordell-Weil Groups of Large Rank in Towersen_US
dc.creatorOcchipinti, Thomasen_US
dc.contributor.authorOcchipinti, Thomasen_US
dc.date.issued2010en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractLet 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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectFunction Fieldsen_US
dc.subjectNumber Theoryen_US
dc.subjectRanksen_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorUlmer, Douglasen_US
dc.contributor.chairUlmer, Douglasen_US
dc.contributor.committeememberSharifi, Romyaren_US
dc.contributor.committeememberCastravet, Ana-Mariaen_US
dc.contributor.committeememberMcCallum, Williamen_US
dc.contributor.committeememberTiep, Pham Hen_US
dc.identifier.proquest10857en_US
dc.identifier.oclc659753763en_US
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