Arithmetic of Quadratic Forms - Shimura, Goro

Topic (A) can be further divided into two types of theories: (a1) Classi?cation over an algebraic number ?eld; At some point we need the Hasse norm theorem for a quadratic extension of a number ?eld, which is included in class ?eld theory. We prove it when the base ?eld is the rational number ?eld to make the book self-contained in that case.