Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction

Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], with Galois group G = Gal(F[infinity]/Q). I show how the p[infinity]-Selmer group of E over F[infinity] controls the p[infinity]-Selmer rank growth within the false Tate curve extension, and how it is connected to the root numbers of E twisted by absolutely irreducible orthogonal Artin representations of G, and investigate the parity conjecture for twisted modules.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2010

Author dc:creator

• Lee, Chern-Yang

• Iwasawa theory
• Parity conjecture
• Elliptic curves

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2bc5ccd0-2a67-4c95-92e7-637e674e7c13/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.16211

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/226462