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| eBook ISBN: | 978-1-4704-2174-8 |
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| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-0-8218-3287-5 |
| eBook: ISBN: | 978-1-4704-2174-8 |
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| AMS Member Price: | $107.20 $81.20 |
| Softcover ISBN: | 978-0-8218-3287-5 |
| Product Code: | ULECT/28 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-2174-8 |
| Product Code: | ULECT/28.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-0-8218-3287-5 |
| eBook ISBN: | 978-1-4704-2174-8 |
| Product Code: | ULECT/28.B |
| List Price: | $134.00 $101.50 |
| MAA Member Price: | $120.60 $91.35 |
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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 well-known 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, co-wrote 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.
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Table of Contents
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Cohomological invariants, Witt invariants, and trace forms
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Contents
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Introduction
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Chapter I. The notion of “invariant”
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Chapter II. Cohomological preliminaries: The local case
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Chapter III. Cohomological preliminaries: The function field case
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Chapter IV. Specialization properties of cohomological invariants
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Chapter V. Restriction and corestriction of invariants
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Chapter VI. Cohomological invariants of O$_n$, SO$_n$,…
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Chapter VII. Cohomological invariants of étale algebras
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Chapter VIII. Witt invariants
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Chapter IX. The trace form in dimension ${}\le 7$
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Appendix A. A letter from M. Rost to J-P. Serre
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Appendix B. A letter from J-P. Serre to R. S. Garibaldi
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Appendix C. A letter from B. Totaro to J-P. Serre
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Rost invariants of simply connected algebraic groups
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Contents
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Rost invariants of simply connected algebraic groups
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Appendix A. The groups $H^{d+1}(F,\mathbb {Q}/\mathbb {Z}(d))$
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Appendix B. Tables of Dynkin indices
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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 well-known 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, co-wrote 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 J-P. Serre
-
Appendix B. A letter from J-P. Serre to R. S. Garibaldi
-
Appendix C. A letter from B. Totaro to J-P. 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
