CM-algebras and CM-types

Abstract: Milne, Complex multiplication, Section 1

We continue our exploration of complex multiplication by studying its building blocks. $K$ is a CM-field iff it is a totally imaginary quadratic extension of a totally real number field. From this definition, we will build up CM-algebras, CM-types and CM-pairs. Following Milne, we also introduce reflex norms and positive involutions.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2026 topic: Explicit class field theory.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.