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. doi:10.7907/8T84-BQ83. https://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.

Thesis Files