Artin L-functions for abelian extensions of imaginary quadratic fields

by Johnson, Jennifer Michelle

Abstract (Summary)
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.
Bibliographical Information:

Advisor:David G. Wales; Mladen Dimitrov; Dinakar Ramakrishnan; Matthias Flach

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis



Date of Publication:05/26/2005

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