Skip to content
Register Sign in Wishlist

Local Cohomology
An Algebraic Introduction with Geometric Applications

2nd Edition

£80.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: November 2012
  • availability: Available
  • format: Hardback
  • isbn: 9780521513630

£ 80.99
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Serre's Affineness Criterion, the Lichtenbaum–Hartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the Fulton–Hansen Connectedness Theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. The book is designed for graduate students who have some experience of basic commutative algebra and homological algebra and also experts in commutative algebra and algebraic geometry. Over 300 exercises are interspersed among the text; these range in difficulty from routine to challenging, and hints are provided for some of the more difficult ones.

    • Gives graduate students a solid grounding in the subject
    • Covers important applications
    • Includes a brand new chapter on 'Canonical Modules'
    Read more

    Reviews & endorsements

    Review of the first edition: '… Brodmann and Sharp have produced an excellent book: it is clearly, carefully and enthusiastically written; it covers all important aspects and main uses of the subject; and it gives a thorough and well-rounded appreciation of the topic's geometric and algebraic interrelationships … I am sure that this will be a standard text and reference book for years to come.' Liam O'Carroll, Bulletin of the London Mathematical Society

    Review of the first edition: 'The book is well organised, very nicely written, and reads very well … a very good overview of local cohomology theory.' Newsletter of the European Mathematical Society

    Review of the first edition: '… a careful and detailed algebraic introduction to Grothendieck's local cohomology theory.' L'Enseignement Mathematique

    '… the book opens the view towards the beauty of local cohomology, not as an isolated subject but as a tool helpful in commutative algebra and algebraic geometry.' Zentralblatt MATH

    'From the point of view of the reviewer (who learned all his basic knowledge about local cohomology reading the first edition of this book and doing some of its exercises), the changes previously described (the new Chapter 12 concerning canonical modules, the treatment of multigraded local cohomology, and the final new section of Chapter 20 about locally free sheaves) definitely make this second edition an even better graduate textbook than the first. Indeed, it is well written and, overall, almost self-contained, which is very important in a book addressed to graduate students.' Alberto F. Boix, Mathematical Reviews

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    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

    • Edition: 2nd Edition
    • Date Published: November 2012
    • format: Hardback
    • isbn: 9780521513630
    • length: 505 pages
    • dimensions: 236 x 157 x 30 mm
    • weight: 0.86kg
    • contains: 330 exercises
    • availability: Available
  • Table of Contents

    Preface to the First Edition
    Preface to the Second Edition
    Notation and conventions
    1. The local cohomology functors
    2. Torsion modules and ideal transforms
    3. The Mayer–Vietoris sequence
    4. Change of rings
    5. Other approaches
    6. Fundamental vanishing theorems
    7. Artinian local cohomology modules
    8. The Lichtenbaum–Hartshorne Theorem
    9. The Annihilator and Finiteness Theorems
    10. Matlis duality
    11. Local duality
    12. Canonical modules
    13. Foundations in the graded case
    14. Graded versions of basic theorems
    15. Links with projective varieties
    16. Castelnuovo regularity
    17. Hilbert polynomials
    18. Applications to reductions of ideals
    19. Connectivity in algebraic varieties
    20. Links with sheaf cohomology
    Bibliography
    Index.

  • Authors

    M. P. Brodmann, Universität Zürich
    M. P. Brodmann is Emeritus Professor in the Institute of Mathematics at the University of Zurich.

    R. Y. Sharp, University of Sheffield
    R. Y. Sharp is Emeritus Professor of Pure Mathematics at the University of Sheffield.

Related Books

also by this author

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 ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

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.
×