An Introduction to Algebraic Number Theory
by F. Oggier
Publisher: Nanyang Technological University 2010
Number of pages: 95
From the table of 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.
Home page url
Download or read it online for free here:
by Henri Darmon, Shou-Wu Zhang - Cambridge University Press
This volume has the Gross-Zagier formula and its avatars as a common unifying theme. It covers the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics.
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.
by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These lecture notes give a rapid introduction to some basic aspects of Algebraic Number Theory with as few prerequisites as possible. Topics: Field Extensions; Ring Extensions; Dedekind Domains and Ramification Theory; Class Number and Lattices.
by Robert B. Ash - University of Illinois
Basic course in algebraic number theory. It covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc.