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Local cohomology: an algebraic introduction with geometric applications


Brodmann, M; Sharp, R Y (2008). Local cohomology: an algebraic introduction with geometric applications. Cambridge: Cambridge University Press.

Abstract

This book provides a careful and detailed algebraic introduction to Grothendieck’s local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo–Mumford regularity, the Fulton–Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

Abstract

This book provides a careful and detailed algebraic introduction to Grothendieck’s local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo–Mumford regularity, the Fulton–Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

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Additional indexing

Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Date:2008
Deposited On:09 Mar 2009 09:08
Last Modified:06 Dec 2017 18:06
Publisher:Cambridge University Press
Series Name:Cambridge Studies in Advanced Mathematics
Volume:60
Number of Pages:436
ISBN:978-0-521-04758-6
Publisher DOI:https://doi.org/10.2277/0521372860
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1613627

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