On the Equivariant Tamagawa Number Conjecture

Citation

Navilarekallu, Tejaswi (2006) On the Equivariant Tamagawa Number Conjecture. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7HZ0-F068. https://resolver.caltech.edu/CaltechETD:etd-05242006-225912

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.

Thesis Files