On the Local Tamagawa Number Conjecture for Tate Motives

Author: Daigle, Gerald Joseph III (Jay)

Year: 2014

Degree: Dissertation (Ph.D.)

Advisor: Flach, Matthias

Committee Members: Flach, Matthias; Ramakrishnan, Dinakar; Mantovan, Elena; Hedayat Zadeh Razavi, S. Mohammad Hadi

Option: Mathematics

DOI: 10.7907/RFXG-4E72

Abstract

There is a wonderful conjecture of Bloch and Kato that generalizes both the analytic Class Number Formula and the Birch and Swinnerton-Dyer conjecture. The conjecture itself was generalized by Fukaya and Kato to an equivariant formulation. In this thesis, I provide a new proof for the equivariant local Tamagawa number conjecture in the case of Tate motives for unramified fields, using Iwasawa theory and (φ,Γ)-modules, and provide some work towards extending the proof to tamely ramified fields.

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