On the Equivariant Tamagawa Number Conjecture

Author: Navilarekallu, Tejaswi

Year: 2006

Degree: Dissertation (Ph.D.)

Advisor: Flach, Matthias

Committee Members: Flach, Matthias; Ramakrishnan, Dinakar; Oh, Hee; Dimitrov, Mladen

Option: Mathematics

DOI: 10.7907/7HZ0-F068

Abstract

For a finite Galois extension K/Q of number fields with Galois group G and a motive M = M' ⊗ h⁰(Spec(K))(0) with coefficients in Q[G], the equivariant Tamagawa number conjecture relates the special value L*(M,0) of the motivic L-function to an element of K₀(Z[G];R) constructed via complexes associated to M. The conjecture for nonabelian groups G is very much unexplored. In this thesis, we will develop some techniques to verify the conjecture for Artin motives and motives attached to elliptic curves. In particular, we consider motives h⁰(Spec(K))(0) for an A₄-extension K/Q and, h¹ (E x Spec(L))(1) for an S₃-extension L/Q and an elliptic curve E/Q.

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