UZH-Logo

Maintenance Infos

Local cohomology: an algebraic introduction with geometric applications


Brodmann, M; Sharp, R (1998). 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.

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.

Altmetrics

Downloads

320 downloads since deposited on 31 May 2010
6 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:ideal transform; local duality; Hilbert polynomials; reduction of ideals; connectivity; sheaf cohomology; vanishing theorems; annihilation; finiteness theorems on local cohomology; Castelnuovo-Mumford regularity
Language:English
Date:1998
Deposited On:31 May 2010 16:09
Last Modified:05 Apr 2016 13:26
Publisher:Cambridge University Press
Series Name:Cambridge Studies in Advanced Mathematics
Volume:60
Number of Pages:416
ISBN:0-521-37286-0
Publisher DOI:https://doi.org/10.2277/0521372860
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1613627
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0903.13006
https://www.zora.uzh.ch/13642/
Permanent URL: https://doi.org/10.5167/uzh-22180

Download

[img]
Preview
Filetype: PDF (Marketing Sample)
Size: 598kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations