Hardcover ISBN:  9780821853498 
Product Code:  CHEL/375.H 
573 pp 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $64.80 
Electronic ISBN:  9780821894002 
Product Code:  CHEL/375.H.E 
573 pp 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $57.60 

Book DetailsAMS Chelsea PublishingVolume: 375; 2012MSC: Primary 14; Secondary 16; 05; 11; 12; 13; 55;
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
ReadershipGraduate students and research mathematicians interested in formal groups and their applications in other areas of mathematics.

Table of Contents

Chapters

Chapter 1. Methods for constructing one dimensional formal groups

Chapter 2. Methods for constructing higher dimensional formal group laws

Chapter 3. Curves, $p$typical formal group laws, and lots of Witt vectors

Chapter 4. Homomorphisms, endomorphisms, and the classification of formal groups by power series methods

Chapter 5. CartierDieudonné modules

Chapter 6. Applications of formal groups in algebraic topology, number theory, and algebraic geometry

Chapter 7. Formal groups and bialgebras

Appendix A. On power series rings

Appendix B. Brief notes on further applications of formal group (law) theory


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This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
Graduate students and research mathematicians interested in formal groups and their applications in other areas of mathematics.

Chapters

Chapter 1. Methods for constructing one dimensional formal groups

Chapter 2. Methods for constructing higher dimensional formal group laws

Chapter 3. Curves, $p$typical formal group laws, and lots of Witt vectors

Chapter 4. Homomorphisms, endomorphisms, and the classification of formal groups by power series methods

Chapter 5. CartierDieudonné modules

Chapter 6. Applications of formal groups in algebraic topology, number theory, and algebraic geometry

Chapter 7. Formal groups and bialgebras

Appendix A. On power series rings

Appendix B. Brief notes on further applications of formal group (law) theory