Group Cohomology and Algebraic Cycles

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

Burt Totaro (Author)

9781107015777, Cambridge University Press

Hardback, published 26 June 2014

246 pages, 2 b/w illus.
22.9 x 15.2 x 1.8 cm, 0.53 kg

'Cohomology of groups is usually developed algebraically via resolutions, and topologically via classifying spaces. This unique and attractively written book develops the subject from the point of view of algebraic geometry … The book is full of computational examples that make accessible what could have been a very abstract subject. It is written at a level that could be used for a graduate course in cohomology of groups.' Mathematical Reviews

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.

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.

Subject Areas: Algebraic topology [PBPD], Topology [PBP], Algebraic geometry [PBMW], Geometry [PBM], Algebra [PBF]