گروه‌های رسمی و کاربردها (انتشارات چلسا AMS)

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. Contents 8 Preface to the corrected printing 12 Preface 14 Introduction 20 1 Methods For Constructing One Dimensional Formal Groups 28 2 Methods For Constructing Higher Dimensional Formal Group Laws 78 3 Curves, P-typical Formal Group Laws, And Lots Of Witt Vectors 118 4 Homomorphisms, Endomorphisms, And The Classification Of Formal Groups By Power Series Methods 174 5 Cartier-dieudonne Modules 339 6 Applications Of Formal Groups In Algebraic Topology, Number Theory, And Algebraic Geometry 454 7 Formal Groups And Bialgebras 505 Appendix A On Power Series Rings 544 Appendix B Brief Notes on Further Applicationsof Formal Group (Law) Theory 550 Notation 578 Bibliography 558 Index 594 FORMAL,GROUPS,AND,APPLICATIONS Provides a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters present basics and main results of the theory, as well as important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary.