Dissertation/Thesis Abstract

On the rank of 2-primary part of Selmer group of certain elliptic curves
by Kim, Kwang Hyun, Ph.D., City University of New York, 2012, 57; 3541487
Abstract (Summary)

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.

Indexing (document details)
Advisor: Kolyvagin, Victor
Commitee: Kramer, Kenneth, Szpiro, Lucien
School: City University of New York
Department: Mathematics
School Location: United States -- New York
Source: DAI-B 74/02(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Elliptic curves, Rank, Selmer groups
Publication Number: 3541487
ISBN: 9781267678287
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