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


Type

Thesis

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Authors

Lee, Chern-Yang 

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.

Description

Date

Advisors

Keywords

Iwasawa theory, Parity conjecture, Elliptic curves

Qualification

Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge