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

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 image arising from the Tate sequence. This conjecture is known to be true for certain non-abelian Galois extensions over image with Galois group being the dihedral or quaternion group. In this article, we shall verify the conjecture for an A4-extension over image, by explicitly constructing the Tate sequence using Chinburgʹs methods.