Burt Totaro

Group Cohomology and Algebraic Cycles (eBook, PDF)

• Format: PDF

Produktbeschreibung

Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights into the Hodge conjecture and algebraic geometry more broadly. This book presents a coherent suite of computational tools for the study of group cohomology and algebraic cycles. Early chapters synthesize background material from topology, algebraic geometry, and commutative algebra so readers do not have to form connections between the literatures on their own. Later chapters demonstrate Peter Symonds's influential proof of David Benson's regularity conjecture, offering several new variants and improvements. Complete with concrete examples and computations throughout, and a list of open problems for further study, this book will be valuable to graduate students and researchers in algebraic geometry and related fields.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. Juni 2014
• Englisch
• ISBN-13: 9781139898423
• Artikelnr.: 40883781

Autorenporträt

Burt Totaro is a Professor of Mathematics at the University of California, Los Angeles. He was elected a Fellow of the Royal Society in 2009.

Inhaltsangabe

Preface
1. Group cohomology
2. The Chow ring of a classifying space
3. Depth and regularity
4. Regularity of group cohomology
5. Generators for the Chow ring
6. Regularity of the Chow ring
7. Bounds for p-groups
8. The structure of group cohomology and the Chow ring
9. Cohomology mod transfers is Cohen-Macaulay
10. Bounds for group cohomology and the Chow ring modulo transfers
11. Transferred Euler classes
12. Detection theorems for cohomology and Chow rings
13. Calculations
14. Groups of order p¿
15. Geometric and topological filtrations
16. The Eilenberg-Moore spectral sequence in motivic cohomology
17. The Chow-Künneth conjecture
18. Open problems.