Kolyvagin proved very remarkable results on Mordell-Weil groups and Shafarevich-Tate groups of certain elliptic curves when a given Heegner point P K has infinite order in his series of papers. He also extended his result to odd prime ℓ-primary part of Selmer group of higher rank with the assumption of existence of non-trivial Kolyvagin system. In this thesis, we will follow his Euler system method and verify that his method also works to prove the result on the rank of 2-primary part of Selmer group of higher rank with Strong non-zero conjecture.
|Commitee:||Kramer, Kenneth, Szpiro, Lucien|
|School:||City University of New York|
|School Location:||United States -- New York|
|Source:||DAI-B 74/02(E), Dissertation Abstracts International|
|Keywords:||Elliptic curves, Rank, Selmer groups|
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