#NumberFields #NumberTheory Does anyone have good references other than Milne for CM fields? I'm up to my ears in them and a few basic properties in a citation-friendy format would go a long way.

It's really frustrating when I should be able to re-derive what I need, but get muddled along the way every time. This should be already done stuff.

Ie. I'm pondering a quandary.

#NumberTheory #Algebraic #NumberFields #cm

Let F CM over ℚ with max real subfield K then α generate F over K, α totally imaginary unit. Take the partial norm of α by the Galois group of K lifted over F; I assert that since it is a generator of an extension, its norm should NOT collapse into ℚ. Thus being a unit it must have its partial norm also a unit, and being totally imaginary in a quadratic extension this must be i.