Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Subject "Iwasawa theory"
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Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-07-06)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], ...
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
(University of CambridgeMathematics, 2017-05-30)The conjecture of Birch and Swinnerton-Dyer is unquestionably one of the most important open problems in number theory today. Let $E$ be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, ...