**Update (January 11, 2014):** Now proofreading. I’ve found a typo in the title of Chapter 8. I misspelled ‘ring’ — pretty humbling. (To give due credit, my editor spotted the typo.)

**Original (December 4, 2013):**

More about the book at the CUP site (it’s not available yet — I’m checking the copyedited manuscript right now).

You can read the preface in manuscript here.

**Contents**

*Preface*

**1** Group cohomology

1.1 Definition of group cohomology

1.2 Equivariant cohomology and basic calculations

1.3 Algebraic definition of group cohomology

**2** The Chow ring of a classifying space

2.1 The Chow group of algebraic cycles

2.2 The Chow ring of a classifying space

2.3 The equivariant Chow ring

2.4 Basic computations

2.5 Transfer

2.6 Becker–Gottlieb transfer for Chow groups

2.7 Groups in characteristic

2.8 Wreath products and the symmetric groups

2.9 General linear groups over finite fields

2.10 Questions about the Chow ring of a finite group

**3** Depth and regularity

3.1 Depth and regularity in terms of local cohomology

3.2 Depth and regularity in terms of generators and relations

3.3 Duflot’s lower bound for depth

**4** Regularity of group cohomology

4.1 Regularity of group cohomology and applications

4.2 Proof of Symonds’s theorem

**5** Generators for the Chow ring

5.1 Bounding the generators of the Chow ring

5.2 Optimality of the bounds

**6** Regularity of the Chow ring

6.1 Bounding the regularity of the Chow ring

6.2 Motivic cohomology

6.3 Steenrod operations on motivic cohomology

6.4 Regularity of motivic cohomology

**7** Bounds for *p*-groups

7.1 Invariant theory of the group **Z** = *p*

7.2 Wreath products

7.3 Bounds for the Chow ring and cohomology of a *p*-group

**8** The structure of group cohomology and the Chow ring

8.1 The norm map

8.2 Quillen’s theorem and Yagita’s theorem

8.3 Yagita’s theorem over any field

8.4 Carlson’s theorem on transfer

**9** Cohomology mod transfers is Cohen–Macaulay

9.1 The Cohen-Macaulay property

9.2 The ring of invariants modulo traces

**10** Bounds for group cohomology and the Chow ring modulo transfers

**11** Transferred Euler classes

11.1 Basic properties of transferred Euler classes

11.2 Generating the Chow ring

**12** Detection theorems for cohomology and Chow rings

12.1 Nilpotence in group cohomology

12.2 The detection theorem for Chow rings

**13** Calculations

13.1 The Chow rings of the groups of order 16

13.2 The modular *p*-group

13.3 Central extensions by *G*_{m}

13.4 The extraspecial group *E*_{p3}

13.5 Calculations of the topological nilpotence degree

**14** Groups of order *p*^{4}

14.1 The wreath product **Z**/3 ≀ **Z**/3

14.2 Geometric and topological filtrations

14.3 Groups of order *p*^{4} for *p* ≥ 5

14.4 Groups of order 81

14.5 A 1-dimensional group

**15** Geometric and topological filtrations

15.1 Summary

15.2 Positive results

15.3 Examples at odd primes

15.4 Examples for *p* = 2

**16** The Eilenberg–Moore spectral sequence in motivic cohomology

16.1 Motivic cohomology of flag bundles

16.2 Leray spectral sequence for a divisor with normal crossings

16.3 Eilenberg-Moore spectral sequence in motivic cohomology

**17** The Chow K¨unneth conjecture

**18** Open problems

*Appendix* Tables

*References*

*Index*