Record:   Prev Next
作者 Brodmann, M. P
書名 Local Cohomology : An Algebraic Introduction with Geometric Applications
出版項 Cambridge : Cambridge University Press, 2012
©2012
國際標準書號 9781139781794 (electronic bk.)
9780521513630
book jacket
版本 2nd ed
說明 1 online resource (516 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Cambridge Studies in Advanced Mathematics ; v.136
Cambridge Studies in Advanced Mathematics
附註 Cover -- Series Page -- Title -- Copyright -- Dedication -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Notation and conventions -- 1 The local cohomology functors -- 1.1 Torsion functors -- 1.2 Local cohomology modules -- 1.3 Connected sequences of functors -- 2 Torsion modules and ideal transforms -- 2.1 Torsion modules -- 2.2 Ideal transforms and generalized ideal transforms -- 2.3 Geometrical significance -- 3 The Mayer-Vietoris sequence -- 3.1 Comparison of systems of ideals -- 3.2 Construction of the sequence -- 3.3 Arithmetic rank -- 3.4 Direct limits -- 4 Change of rings -- 4.1 Some acyclic modules -- 4.2 The Independence Theorem -- 4.3 The Flat Base Change Theorem -- 5 Other approaches -- 5.1 Use of Čech complexes -- 5.2 Use of Koszul complexes -- 5.3 Local cohomology in prime characteristic -- 6 Fundamental vanishing theorems -- 6.1 Grothendieck's Vanishing Theorem -- 6.2 Connections with grade -- 6.3 Exactness of ideal transforms -- 6.4 An Affineness Criterion due to Serre -- 6.5 Applications to local algebra in prime characteristic -- 7 Artinian local cohomology modules -- 7.1 Artinian modules -- 7.2 Secondary representation -- 7.3 The Non-vanishing Theorem again -- 8 The Lichtenbaum-Hartshorne Theorem -- 8.1 Preparatory lemmas -- 8.2 The main theorem -- 9 The Annihilator and Finiteness Theorems -- 9.1 Finiteness dimensions -- 9.2 Adjusted depths -- 9.3 The first inequality -- 9.4 The second inequality -- 9.5 The main theorems -- 9.6 Extensions -- 10 Matlis duality -- 10.1 Indecomposable injective modules -- 10.2 Matlis duality -- 11 Local duality -- 11.1 Minimal injective resolutions -- 11.2 Local Duality Theorems -- 12 Canonical modules -- 12.1 Definition and basic properties -- 12.2 The endomorphism ring -- 12.3 S2-ifications -- 13 Foundations in the graded case
13.1 Basic multi-graded commutative algebra -- 13.2 *Injective modules -- 13.3 The *restriction property -- 13.4 The reconciliation -- 13.5 Some examples and applications -- 14 Graded versions of basic theorems -- 14.1 Fundamental theorems -- 14.2 *Indecomposable *injective modules -- 14.4 Graded local duality -- 14.3 A graded version of the Annihilator Theorem -- 14.5 *Canonical modules -- 15 Links with projective varieties -- 15.1 Affine algebraic cones -- 15.2 Projective varieties -- 16 Castelnuovo regularity -- 16.1 Finitely generated components -- 16.2 The basics of Castelnuovo regularity -- 16.3 Degrees of generators -- 17 Hilbert polynomials -- 17.1 The characteristic function -- 17.2 The significance of reg2 -- 17.3 Bounds on reg2 in terms of Hilbert coefficients -- 17.4 Bounds on reg1 and reg0 -- 18 Applications to reductions of ideals -- 18.1 Reductions and integral closures -- 18.2 The analytic spread -- 18.3 Links with Castelnuovo regularity -- 19 Connectivity in algebraic varieties -- 19.1 The connectedness dimension -- 19.2 Complete local rings and connectivity -- 19.3 Some local dimensions -- 19.4 Connectivity of affine algebraic cones -- 19.5 Connectivity of projective varieties -- 19.6 Connectivity of intersections -- 19.7 The projective spectrum and connectedness -- 20 Links with sheaf cohomology -- 20.1 The Deligne Isomorphism -- 20.2 The Graded Deligne Isomorphism -- 20.3 Links with sheaf theory -- 20.4 Applications to projective schemes -- 20.5 Locally free sheaves -- References -- Index
This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Brodmann, M. P. Local Cohomology : An Algebraic Introduction with Geometric Applications Cambridge : Cambridge University Press,c2012 9780521513630
主題 Algebra, Homological.;Sheaf theory.;Commutative algebra
Electronic books
Alt Author Sharp, R. Y
Record:   Prev Next