Heegner Points and Rankin L-Series
by Henri Darmon, Shou-Wu Zhang
Publisher: Cambridge University Press 2004
Number of pages: 382
This volume, based on a workshop on Special Values of Rankin L-Series held at the MSRI in December 2001, is a collection of articles written by many of the leading contributors in the field, having the Gross-Zagier formula and its avatars as a common unifying theme. It serves as a valuable reference for mathematicians wishing to become better acquainted with the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.
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by J.S. Milne
Contents: Preliminaries From Commutative Algebra; Rings of Integers; Dedekind Domains; Factorization; The Finiteness of the Class Number; The Unit Theorem; Cyclotomic Extensions; Fermat's Last Theorem; Valuations; Local Fields; Global Fields.
by F. Oggier - Nanyang Technological University
Contents: Algebraic numbers and algebraic integers (Rings of integers, Norms and Traces); Ideals (Factorization and fractional ideals, The Chinese Theorem); Ramification theory; Ideal class group and units; p-adic numbers; Valuations; p-adic fields.
by Steve Wright - arXiv
This is a series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required.
by J. S. Milne
These are preliminary notes for a modern account of the theory of complex multiplication. The reader is expected to have a good knowledge of basic algebraic number theory, and basic algebraic geometry, including abelian varieties.