Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Group Cohomology and Algebraic Cycles
  • Cited by 33
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      05 March 2014
      26 June 2014
      ISBN:
      9781139059480
      9781107015777
      DOI:
      https://doi.org/10.1017/CBO9781139059480
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.53kg, 246 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology, Algebra
      Series:
      Cambridge Tracts in Mathematics (204)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Tracts in Mathematics (204)
    Information

    Book description

    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.

    Reviews

    '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.'

    Source: Mathematical Reviews

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents
    References

    Metrics

    Altmetric attention score

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.