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Local cohomology : an algebraic introduction with geometric applications

Author: M P Brodmann; R Y Sharp
Publisher: Cambridge : Cambridge University Press, 2013.
Series: Cambridge studies in advanced mathematics, 136
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Document Type: Book
All Authors / Contributors: M P Brodmann; R Y Sharp
ISBN: 9780521513630 0521513634
OCLC Number: 854848319
Description: xxii, 491 pages : illustrations ; 24 cm.
Contents: 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.
Series Title: Cambridge studies in advanced mathematics, 136
Responsibility: M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield.

Abstract:

This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field.  Read more...

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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 Read more...

 
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