Mathematics MS Thesis Defense by Enis Kaya

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KOÇ UNIVERSITY

GRADUATE SCHOOL OF SCIENCES & ENGINEERING

MATHEMATICS

MS THESIS DEFENSE BY ENİS KAYA

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Title: On Extended Selmer Groups for Coleman Deformations

Speaker: Enis Kaya

Time: August 14, 2017, 15:00

Place: ENG 127

Koç University

Rumeli Feneri Yolu

Sariyer, Istanbul

Thesis Committee Members:

Assoc. Prof. Kâzım Büyükboduk (Advisor, Koç University)

Prof. Varga Kalantarov (Koç University)

Prof. K. İlhan İkeda (Yeditepe University)

Abstract:

In 2017, Bharathwaj Palvannan proved a factorization formula involving Selmer groups, predicted by the main conjectures of Iwasawa theory for several Galois representations, corresponding to a factorization formula involving p-adic L-functions proved by Samit Dasgupta in 2014. Bharathwaj Palvannan started with the Galois representation associated to a Hida family that satisfies a highly restrictive ordinariness hypothesis, namely Panchiskin condition. The purpose of this thesis is to discuss a potential non-ordinary generalization of Bharathwaj Palvannan’s result following Jonathan Pottharst who gave a vast generalization of Panchiskin condition to the non-ordinary setting. Our ultimate goal is to form the extended Selmer groups emerging from the non-ordinary Galois representation attached to a Coleman family.