Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
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Authors
Lee, Chern-Yang
Advisors
Coates, John
Date
2010-07-06Awarding Institution
University of Cambridge
Author Affiliation
Department of Pure Mathematics and Mathematical Statistics
Qualification
Doctor of Philosophy (PhD)
Language
English
Type
Thesis
Metadata
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Lee, C. (2010). Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction (Doctoral thesis). https://doi.org/10.17863/CAM.16211
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
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