Local Cohomology (Hardcover) (ISBN-13: 9780521513630)

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.

Author: M. P. Brodmann
ISBN-10: 0521513634
ISBN-13: 9780521513630
Publisher: Cambridge University Press
Language: English
Published: 11/15/2012
Pages: 505
Format: Hardcover
Weight: 1.85lbs
Size: 9.10h x 6.00w x 1.20d