(0) items

Local Cohomology: An Algebraic Introduction with Geometric Applications,9780521513630
This item qualifies for

Your order must be $59 or more, you must select US Postal Service Shipping as your shipping preference, and the "Group my items into as few shipments as possible" option when you place your order.

Bulk sales, PO's, Marketplace Items, eBooks, Apparel, and DVDs not included.

Local Cohomology: An Algebraic Introduction with Geometric Applications



Pub. Date:
Cambridge University Press

Questions About This Book?

Why should I rent this book?
Renting is easy, fast, and cheap! Renting from can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.
How do rental returns work?
Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!
What version or edition is this?
This is the 2nd edition with a publication date of 1/7/2013.
What is included with this book?
  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.
  • The eBook copy of this book is not guaranteed to include any supplemental materials. Typically only the book itself is included.


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.

Table of Contents

Preface to the First Edition
Preface to the Second Edition
Notation and conventions
The local cohomology functors
Torsion modules and ideal transforms
The Mayer-Vietoris sequence
Change of rings
Other approaches
Fundamental vanishing theorems
Artinian local cohomology modules
The Lichtenbaum-Hartshorne Theorem
The Annihilator and Finiteness Theorems
Matlis duality
Local duality
Canonical modules
Foundations in the graded case
Graded versions of basic theorems
Links with projective varieties
Castelnuovo regularity
Hilbert polynomials
Applications to reductions of ideals
Connectivity in algebraic varieties
Links with sheaf cohomology
Table of Contents provided by Publisher. All Rights Reserved.

Please wait while the item is added to your cart...