Period, index and potential sha
| dc.creator | Clark, Pete L. | |
| dc.creator | Sharif, Shahed | |
| dc.date | 2008-11-18 | |
| dc.date.accessioned | 2026-07-07T10:19:26Z | |
| dc.date.available | 2026-07-07T10:19:26Z | |
| dc.description | In this paper we advance the theory of O'Neil's period-index obstruction map and derive consequences for the arithmetic of genus one curves over global fields. Our first result implies that for every pair of positive integers (P,I) with P dividing I and I dividing P^2, there exists a number field K and a genus one curve C over K with period P and index I. Second, let E be any elliptic curve over a global field K, and let P > 1 be any integer indivisible by the characteristic of K. We construct infinitely many genus one curves C over K with period P, index P^2, and Jacobian E. We deduce strong consequences on the structure of Sharevich-Tate groups under field extension. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0811.3019 | |
| dc.identifier | http://arxiv.org/abs/0811.3019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174506 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Period, index and potential sha | |
| dc.type | text |