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On the Local Tamagawa Number Conjecture for Tate Motives


Daigle, Gerald Joseph III (Jay) (2014) On the Local Tamagawa Number Conjecture for Tate Motives. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RFXG-4E72.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics, number theory, L-functions, (phi, Gamma)-modules
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Flach, Matthias
Thesis Committee:
  • Flach, Matthias (chair)
  • Ramakrishnan, Dinakar
  • Mantovan, Elena
  • Hedayat Zadeh Razavi, S. Mohammad Hadi
Defense Date:21 May 2014
Record Number:CaltechTHESIS:05292014-153502602
Persistent URL:
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Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8427
Deposited By: Gerald Daigle
Deposited On:30 May 2014 23:57
Last Modified:04 Oct 2019 00:05

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