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On the Tamagawa Number Conjecture for Motives Attached to Modular Forms


Gealy, Matthew Thomas (2006) On the Tamagawa Number Conjecture for Motives Attached to Modular Forms. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/X671-G590.


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
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2006. Scott Russell Johnson Prize for Excellence in Graduate Study in Mathematics, 2002, 2004.
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:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5020
Deposited By: Imported from ETD-db
Deposited On:19 Dec 2005
Last Modified:18 Dec 2020 19:15

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