Del 136 i serien Cambridge Studies in Advanced Mathematics

Local Cohomology

An Algebraic Introduction with Geometric Applications

Inbunden, Engelska, 2012

1 509 kr

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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.

Produktinformation

Utgivningsdatum2012-11-15
Mått157 x 236 x 30 mm
Vikt860 g
FormatInbunden
SpråkEngelska
SerieCambridge Studies in Advanced Mathematics
Antal sidor505
Upplaga2
FörlagCambridge University Press
ISBN9780521513630

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Algebra inom Naturvetenskap och teknik

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.

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