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Title: Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
Author: Lee, Chern-Yang
ISNI:       0000 0004 2707 4085
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2010
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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 groupG = 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.
Supervisor: Coates, John Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: Iwasawa theory ; Parity conjecture ; Elliptic curves