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Title: On Howard's main conjecture and the Heegner point Kolyvagin system
Authors: Zanarella, Murilo
Advisors: Skinner, Christopher
Castella, Francesc
Department: Mathematics
Class Year: 2019
Abstract: We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. As in the recent result of Burungale, Castella and Kim, we do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture but, unlike their result, we do not restrict ourselves to the case of analytic rank 1 over K. The main ingredient for this is an improvement of Howard's Kolyvagin system formalism. As another consequence of this improvement, we establish the equivalence between this main conjecture and the primitivity of the Kolyvagin system in certain cases, by also exploiting a explicit reciprocity law for Heegner points.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

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