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

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##### Authors

Lee, Chern-Yang

##### Advisors

Coates, John

##### Date

2010-07-06##### Awarding Institution

University of Cambridge

##### Author Affiliation

Department of Pure Mathematics and Mathematical Statistics

##### Qualification

PhD

##### Language

English

##### Type

Thesis

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Show full item record##### Citation

Lee, C. (2010). Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction (doctoral thesis).

##### 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
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.

##### Keywords

Iwasawa theory, Parity conjecture, Elliptic curves

##### Identifiers

This record's URL: http://www.dspace.cam.ac.uk/handle/1810/226462