Artin L-Functions for Abelian Extensions of Imaginary Quadratic Fields

Author: Johnson, Jennifer Michelle

Year: 2005

Degree: Dissertation (Ph.D.)

Advisor: Flach, Matthias

Committee Members: Flach, Matthias; Wales, David B.; Ramakrishnan, Dinakar; Dimitrov, Mladen

Option: Mathematics; Chemistry

DOI: 10.7907/8T84-BQ83

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.

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