Local Cohomology An Algebraic Introduction with Geometric Applications 2nd Edition by Brodmann, Sharp ISBN 978-1139780315 1139780315
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Local Cohomology An Algebraic Introduction with Geometric Applications 2nd Edition by Brodmann M.P., R. Y. Sharp – Ebook PDF Instant Download/Delivery: 978-1139780315, 1139780315
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Product details:
ISBN 10: 1139780315
ISBN 13: 978-1139780315
Author: Brodmann M.P., R. Y. Sharp
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:
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
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Tags: Brodmann, Sharp, Local Cohomology, An Algebraic Introduction, Geometric Applications