dc.contributor.advisor | Schmidt, Ralf | |
dc.contributor.author | Turki, Salam | |
dc.date.accessioned | 2015-08-12T20:47:46Z | |
dc.date.available | 2015-08-12T20:47:46Z | |
dc.date.issued | 2015 | |
dc.identifier.uri | https://hdl.handle.net/11244/15500 | |
dc.description.abstract | The goal of this dissertation is to find the irreducible, admissible representation
of GL(2; F) attached to an elliptic curve E over a p-adic field F. Associated
to E is a 2-dimensional complex representation of the Weil-Deligne group
via the action of the absolute Galois group on the Tate module. On
the other hand, the local Langlands correspondence states that the 2-dimensional
representations of the Weil-Deligne group are in bijection with equivalence classes of irreducible, admissible representations of GL(2; F). We consider a Weierstrass equation for E of the form
y2 + a1xy + a2y = x3 + a2x2 + a4x + a6 (W)
We will determine the representation the p-adic field in terms of the coefficients a1; a2; a3; a4; a6.
We also investigate a particular class of these reperesentations called "triply imprimitive" representations. | en_US |
dc.language | en_US | en_US |
dc.subject | Elliptic curves, representation theorey, p-adic fields | en_US |
dc.title | The representations of p-adic fields associated to elliptic curves | en_US |
dc.contributor.committeeMember | Kujawa, Jonathan | |
dc.contributor.committeeMember | Martin, Kimball | |
dc.contributor.committeeMember | Roche, Alan | |
dc.contributor.committeeMember | Dunn, Anne | |
dc.date.manuscript | 2015-08-12 | |
dc.thesis.degree | Ph.D. | en_US |
ou.group | College of Arts and Sciences::Department of Mathematics | en_US |
shareok.nativefileaccess | restricted | en_US |