Local cohomology : an algebraic introduction with geometric applications
 Responsibility
 M.P. Brodmann, R.Y. Sharp.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2013.
 Physical description
 xxii, 491 p. : ill. ; 24 cm.
 Series
 Cambridge studies in advanced mathematics ; 136.
Access
Creators/Contributors
 Author/Creator
 Brodmann, M. P. (Markus P.), 1945
 Contributor
 Sharp, R. Y.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [480]484) and index.
 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 MayerVietoris sequence 4. Change of rings 5. Other approaches 6. Fundamental vanishing theorems 7. Artinian local cohomology modules 8. The LichtenbaumHartshorne 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multigraded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasiaffine and quasiprojective varieties. Topics covered include Serre's Affineness Criterion, the LichtenbaumHartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the FultonHansen 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Algebra, Homological.
Bibliographic information
 Publication date
 2013
 Series
 Cambridge studies in advanced mathematics ; 136
 Note
 Previous ed.: 1998.
 ISBN
 9780521513630 (hbk.)
 0521513634 (hbk.)
 9781139044059 (ebook)
 1139044052 (ebook)