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Artin L-functions for abelian extensions of imaginary quadratic fields

Citation

Johnson, Jennifer Michelle (2005) Artin L-functions for abelian extensions of imaginary quadratic fields. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06062005-134908

Abstract

Let F be an abelian extension of an imaginary quadratic field K with Galois group G. We form the Galois-equivariant L-function of the motive h(Spec F)(j) where the Tate twists j are negative integers. The leading term in the Taylor expansion at s=0 decomposes over the group algebra Q[G] into a product of Artin L-functions indexed by the characters of G. We construct a motivic element via the Eisenstein symbol and relate the L-value to periods via regulator maps. Working toward the equivariant Tamagawa number conjecture, we prove that the L-value gives a basis in etale cohomology which coincides with the basis given by the p-adic L-function according to the main conjecture of Iwasawa theory.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Euler system; imaginary quadratic fields; L-functions; Tamagawa number conjecture
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)
  • Wales, David B.
  • Ramakrishnan, Dinakar
  • Dimitrov, Mladen
Defense Date:26 May 2005
Record Number:CaltechETD:etd-06062005-134908
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-06062005-134908
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2475
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:06 Jun 2005
Last Modified:26 Dec 2012 02:51

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