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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/194213 |
| Date | January 2010 |
| Creators | Occhipinti, Thomas |
| Contributors | Ulmer, Douglas, Ulmer, Douglas, Sharifi, Romyar, Castravet, Ana-Maria, McCallum, William, Tiep, Pham H |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| 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. |
Page generated in 0.0023 seconds