Algebraic Number Theory

✍ Scribed by A. Fröhlich, M. J. Taylor

• Publisher: Cambridge University Press
• Year: 1992
• Tongue: English
• Leaves: 371
• Series: Cambridge Studies in Advanced Mathematics 27
• Category: Library

✦ Synopsis

It is an unfortunate feature of number theory that few of the books explain clearly the motivation for much of the technology introduced. Similarly, half of this book is spent proving properties of Dedekind domains before we see much motivation.

That said, there are quite a few examples, as well as some concrete and enlightening exercises (in the back of the book, separated by chapter). There is also a chapter, if the reader is patient enough for it, on Diophantine equations, which gives a good sense of what all this is good for.

The perspective of the book is global. Central themes are the calculation of the class number and unit group. The finiteness of the class number and Dirichlet's Unit Theorem are both proved. L-functions are also introduced in the final chapter.

While the instructor should add more motivation earlier, the book is appropriate for a graduate course in number theory, for students who already know, for instance, the classification of finitely generated modules over a PID. It may be better than others, but would be difficult to use for self-study without additional background.