CaltechTHESIS
  A Caltech Library Service

On the local Tamagawa number conjecture for Tate motives

Citation

Daigle, Gerald Joseph III (Jay) (2014) On the local Tamagawa number conjecture for Tate motives. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05292014-153502602

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.

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:http://resolver.caltech.edu/CaltechTHESIS:05292014-153502602
Related URLs:
URLURL TypeDescription
http://jaydaigle.netAuthorUNSPECIFIED
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8427
Collection:CaltechTHESIS
Deposited By: Gerald Daigle
Deposited On:30 May 2014 23:57
Last Modified:19 Apr 2017 18:36

Thesis Files

[img]
Preview
PDF - Final Version
See Usage Policy.

494Kb

Repository Staff Only: item control page