Artin L-Functions for Abelian Extensions of Imaginary Quadratic Fields

Euler system;imaginary quadratic fields;L-functions;Tamagawa number conjecture

Johnson, Jennifer Michelle ; Flach, Matthias

University:California Institute of Technology

Department:Physics, Mathematics and Astronomy

关键词: Euler system;    imaginary quadratic fields;    L-functions;    Tamagawa number conjecture;   

Others  :  https://thesis.library.caltech.edu/2475/2/thesis.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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.