Local Cohomology

An Algebraic Introduction with Geometric Applications

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Local Cohomology by M. P. Brodmann, R. Y. Sharp, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: M. P. Brodmann, R. Y. Sharp ISBN: 9781139793186
Publisher: Cambridge University Press Publication: November 15, 2012
Imprint: Cambridge University Press Language: English
Author: M. P. Brodmann, R. Y. Sharp
ISBN: 9781139793186
Publisher: Cambridge University Press
Publication: November 15, 2012
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book July Crisis by M. P. Brodmann, R. Y. Sharp
Cover of the book Music and Ceremonial at British Coronations by M. P. Brodmann, R. Y. Sharp
Cover of the book A Short Course in Computational Science and Engineering by M. P. Brodmann, R. Y. Sharp
Cover of the book Modern Statistical Methods for Astronomy by M. P. Brodmann, R. Y. Sharp
Cover of the book Human Rights in Africa by M. P. Brodmann, R. Y. Sharp
Cover of the book The Sins of the Nation and the Ritual of Apologies by M. P. Brodmann, R. Y. Sharp
Cover of the book Legal Authority beyond the State by M. P. Brodmann, R. Y. Sharp
Cover of the book The Stages of Economic Growth by M. P. Brodmann, R. Y. Sharp
Cover of the book The Cambridge Companion to Literature and the Posthuman by M. P. Brodmann, R. Y. Sharp
Cover of the book Ethical Naturalism by M. P. Brodmann, R. Y. Sharp
Cover of the book Making Prussians, Raising Germans by M. P. Brodmann, R. Y. Sharp
Cover of the book Democracy and Moral Conflict by M. P. Brodmann, R. Y. Sharp
Cover of the book Fractional Freedoms by M. P. Brodmann, R. Y. Sharp
Cover of the book Strategic Management by M. P. Brodmann, R. Y. Sharp
Cover of the book Meaning and Power in the Language of Law by M. P. Brodmann, R. Y. Sharp
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy