Structure of some integral Galois representations

Artin formalism gives an equality of certain L-functions of elliptic curves or of zeta-functions of number fields. When combined with the Birch and Swinnerton-Dyer conjecture, this can give interesting results about the Galois module structure of the Selmer group of an elliptic curve. When combined with the analytic class number formula, this can help determine the Galois module structure of the group of units of a number field. In this talk, I will introduce the main technique, which is completely representation theoretic, for extracting such information