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On the Tamagawa Number Conjecture for motives attached to modular forms

Citation

Gealy, Matthew Thomas (2006) On the Tamagawa Number Conjecture for motives attached to modular forms. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-12162005-124435

Abstract

We carry out certain automorphic and l-adic computations, the former extending results of Beilinson and Scholl, and the latter using ideas of Kato and Kings, related to explicit motivic cohomology classes on modular varieties. Under mild local and global conditions on a modular form, these give exactly the coordinates of the Deligne and l-adic realizations of said motivic cohomology class in the eigenspace attached to the modular form (Theorem 4.1.1). Assuming Kato's Main Conjecture and a Leopoldt-type conjecture, we deduce (a weak version of) the Tamagawa Number Conjecture for the motive attached to a modular form, twisted by a negative integer.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:L-functions; L-values
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
  • Wambach, Eric
  • Oh, Hee
Defense Date:8 December 2005
Record Number:CaltechETD:etd-12162005-124435
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-12162005-124435
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5020
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:19 Dec 2005
Last Modified:26 Dec 2012 03:13

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