On the equivariant Tamagawa number conjecture for A4-extensions of number fields

For a finite Galois extension K/k of number fields, with Galois group G, the equivariant Tamagawa number conjecture of Burns and Flach relates the leading coefficients of Artin L-functions to an element of K0(Z[G],R) arising from the Tate sequence. This conjecture is known to be true for certain non-abelian Galois extensions over Q with Galois group being the dihedral or quaternion group. In this article, we shall verify the conjecture for an A4-extension over Q, by explicitly constructing the Tate sequence using Chinburg's methods.