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4 votes

Fields whose embeddings into the complex numbers are invariant under complex conjugation

The only fields with this property are algebraic over $\mathbb{Q}$. They are either totally real or a quadratic imaginary extension of a totally real field (but not necessarily finite). Proof: Note t …
Kevin Ventullo's user avatar
10 votes

Where does the principal ideal theorem (from CFT) go?

There is a generalization of the principal ideal theorem to ray class groups: Let $K$ be a number field, $\mathfrak{m}$ a modulus for $K$, $L:=K(\mathfrak{m})$ the ray class field modulo $\mathfrak{ …
Kevin Ventullo's user avatar