Local Cohomology
An Algebraic Introduction with Geometric Applications
M. P. Brodmann, R. Y. Sharp
- English
- PDF
- Disponible sur iOS et Android
Local Cohomology
An Algebraic Introduction with Geometric Applications
M. P. Brodmann, R. Y. Sharp
Ă propos de ce livre
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 LichtenbaumâHartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the FultonâHansen 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.