The fundamental theorem of complex multiplication
J.S. Milne

TL;DR
This paper provides a straightforward and elementary proof of the fundamental theorem of complex multiplication, clarifying its core concepts and historical development for a broad mathematical audience.
Contribution
It offers a simplified, accessible proof of the fundamental theorem of complex multiplication, enhancing understanding of its foundational role in number theory.
Findings
A clear, elementary proof of the theorem is presented.
The proof consolidates various complex multiplication results into a unified argument.
The article clarifies the theorem's significance in the context of algebraic number theory.
Abstract
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of part of my manuscript, Complex Multiplication, April 7, 2006.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Algebra and Geometry
