Skip to content
Cart

Your Cart

×

You have 0 items in your cart.

Register Sign in Wishlist

Group Cohomology and Algebraic Cycles

$88.00 (C)

Part of Cambridge Tracts in Mathematics

  • Author: Burt Totaro, University of California, Los Angeles
  • Date Published: June 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107015777
Average user rating
(1 review)

$ 88.00 (C)
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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.

    • Contains many concrete examples and computations
    • Early chapters synthesize background material from topology, algebraic geometry and commutative algebra
    • Includes a list of open problems at the end
    Read more

    Reviews & endorsements

    "The author is one of the world experts on the Chow ring of algebraic cycles on the classifying space of an algebraic group and its interplay with the classical mod p cohomology ring. With a focus on finite groups, this text develops in parallel the theory of these two important families of rings. Very recent results about deep structural properties are presented here for the first time in book form, including, notably, Symonds’s calculation of the Castelnuovo–Mumford regularity of group cohomology and its consequences. Some results about group cohomology are improvements on the literature, and many of the parallel results about Chow rings are new. The book is recommended for advanced students and researchers interested in seeing some of the lovely ways in which representation theory, algebraic topology, algebraic geometry, and commutative algebra fruitfully interact."
    Nicholas Kuhn, University of Virginia

    "This attractively written book provides a very readable and up-to-date account of the cohomology of groups. The emphasis is on the geometric point of view provided by the Chow ring of the classifying space. A particularly nice feature is that Symonds’s recent proof of the regularity conjecture and several of its generalizations are discussed in detail."
    David J. Benson, University of Aberdeen

    "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

    See more reviews

    Customer reviews

    13th Sep 2015 by CUPEditorial

    MAA Reviews, Felipe Zaldivar [stars not assigned by MAA]: "This important monograph collects in a systematic way, and in some cases improves on, most of the recent developments in [group cohomology]. ... The whole book emphasizes the advantages provided by the algebro-geometric approach to group cohomology, and at the same time gives new perspectives to important open questions on algebraic geometry. Even taking into account the high level of the subject, the exposition is nicely systematic, making it accessible to graduate students and researchers in adjacent areas, and even including a chapter on open problems." http://www.maa.org/press/maa-reviews/group-cohomology-and-algebraic-cycles

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: June 2014
    • format: Hardback
    • isbn: 9781107015777
    • length: 246 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.53kg
    • contains: 2 b/w illus.
    • availability: Available
  • Table of Contents

    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 p⁴
    15. Geometric and topological filtrations
    16. The Eilenberg–Moore spectral sequence in motivic cohomology
    17. The Chow–Künneth conjecture
    18. Open problems.

  • Author

    Burt Totaro, University of California, Los Angeles
    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.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×