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Softcover ISBN:  9780821832875 
Product Code:  ULECT/28 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421748 
Product Code:  ULECT/28.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821832875 
eBook ISBN:  9781470421748 
Product Code:  ULECT/28.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 28; 2003; 168 ppMSC: Primary 12; 11
This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field.
The authors are wellknown experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, cowrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here.
The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number theory and Galois cohomology.
ReadershipGraduate students and research mathematicians interested in number theory and Galois cohomology.

Table of Contents

Cohomological invariants, Witt invariants, and trace forms

Contents

Introduction

Chapter I. The notion of “invariant”

Chapter II. Cohomological preliminaries: The local case

Chapter III. Cohomological preliminaries: The function field case

Chapter IV. Specialization properties of cohomological invariants

Chapter V. Restriction and corestriction of invariants

Chapter VI. Cohomological invariants of O$_n$, SO$_n$,…

Chapter VII. Cohomological invariants of étale algebras

Chapter VIII. Witt invariants

Chapter IX. The trace form in dimension ${}\le 7$

Appendix A. A letter from M. Rost to JP. Serre

Appendix B. A letter from JP. Serre to R. S. Garibaldi

Appendix C. A letter from B. Totaro to JP. Serre

Rost invariants of simply connected algebraic groups

Contents

Rost invariants of simply connected algebraic groups

Appendix A. The groups $H^{d+1}(F,\mathbb {Q}/\mathbb {Z}(d))$

Appendix B. Tables of Dynkin indices


Additional Material

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This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field.
The authors are wellknown experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, cowrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here.
The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number theory and Galois cohomology.
Graduate students and research mathematicians interested in number theory and Galois cohomology.

Cohomological invariants, Witt invariants, and trace forms

Contents

Introduction

Chapter I. The notion of “invariant”

Chapter II. Cohomological preliminaries: The local case

Chapter III. Cohomological preliminaries: The function field case

Chapter IV. Specialization properties of cohomological invariants

Chapter V. Restriction and corestriction of invariants

Chapter VI. Cohomological invariants of O$_n$, SO$_n$,…

Chapter VII. Cohomological invariants of étale algebras

Chapter VIII. Witt invariants

Chapter IX. The trace form in dimension ${}\le 7$

Appendix A. A letter from M. Rost to JP. Serre

Appendix B. A letter from JP. Serre to R. S. Garibaldi

Appendix C. A letter from B. Totaro to JP. Serre

Rost invariants of simply connected algebraic groups

Contents

Rost invariants of simply connected algebraic groups

Appendix A. The groups $H^{d+1}(F,\mathbb {Q}/\mathbb {Z}(d))$

Appendix B. Tables of Dynkin indices