dc.contributor.advisor Coates, John dc.contributor.author Lee, Chern-Yang dc.date.accessioned 2010-09-23T15:20:17Z dc.date.available 2010-09-23T15:20:17Z dc.date.issued 2010-07-06 dc.identifier.other PhD.33398 dc.identifier.uri http://www.dspace.cam.ac.uk/handle/1810/226462 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/226462 dc.description.abstract 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 en_GB 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. dc.language.iso en en_GB dc.subject Iwasawa theory en_GB dc.subject Parity conjecture en_GB dc.subject Elliptic curves en_GB dc.title Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction en_GB dc.type Thesis en_GB dc.type.qualificationlevel Doctoral dc.type.qualificationname Doctor of Philosophy (PhD) dc.publisher.institution University of Cambridge en_GB dc.publisher.department Department of Pure Mathematics and Mathematical Statistics en_GB dc.identifier.doi 10.17863/CAM.16211
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