INTRODUCTION TO CYCLOTOMIC FIELDS WASHINGTON PDF
Buy Introduction to Cyclotomic Fields (Graduate Texts in Mathematics) on ✓ FREE SHIPPING on qualified Lawrence C. Washington (Author ). Introduction to Cyclotomic Fields has 4 ratings and 2 reviews. Dan said: This book is not as important as the point that this book represents.I was tak. Right now, I am reading Larry Washington’s book “Introduction to Cyclotomic Fields.” In Chapter 8 of this book, the unit group of the ring of.
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The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa’s theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory though one of my students took such a course concurrently.
In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification …mehr.
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Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix.
For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class washiington, and variants of this statement.
The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic.
After that, the reader willing to washinhton occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions.
Introduction to Cyclotomic Fields (eBook, PDF) von Lawrence C. Washington – Portofrei bei
The last chapter, on inttoduction Kronecker-Weber theorem, can be read after Chapter 2. The p adic regulator. Applications of the class number formula. The index of the Stickelberger ideal. Group rings and power series. Proof of the p adic class number formula. Some theorems on class groups.
Introduction to Cyclotomic Fields
Consequences of Vandiver’s conjecture. The estimate for even characters. The estimate for all characters. The estimate for hm. Odlyzko’s bounds on discriminants.
The structure of A nitroduction. The maximal abelian p extension unramified outside p. Local units modulo cyclotomic units. The converse of Herbrand’s theorem. Technical results from Iwasawa theory. Proof of the Main Conjecture.
Primality testing using Jacobi sums. Infinite Galois theory and ramification theory. Proof of the p-adic class number formula. The estimate for hm. The structure of A-modules. The maximal abelian p-extension unramified outside p.