Multiplicities and chern classes in local algebra:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1998
|
Ausgabe: | 1. publ. |
Schriftenreihe: | Cambridge tracts in mathematics
133 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XI, 303 S. |
ISBN: | 0521473160 |
Internformat
MARC
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100 | 1 | |a Roberts, Paul Christopher |e Verfasser |4 aut | |
245 | 1 | 0 | |a Multiplicities and chern classes in local algebra |c Paul C. Roberts |
250 | |a 1. publ. | ||
264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1998 | |
300 | |a XI, 303 S. | ||
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Datensatz im Suchindex
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adam_text | Contents
Preface page ix
Part One: Multiplicities 1
1 Prime Ideals and the Chow Group 3
1.1 Prime Ideals in Noetherian Rings 3
1.2 Cycles and the Chow Group 7
2 Graded Rings and Samuel Multiplicity 18
2.1 Graded Rings and Hilbert Polynomials 18
2.2 Rees Rings and Associated Graded Rings 26
2.3 Dimension Theory in Local Rings 28
2.4 The Samuel Multiplicity of an Ideal 32
2.5 Mixed Multiplicities and Buchsbaum Rim Multiplicities 36
3 Complexes and Derived Functors 42
3.1 Derived Functors 42
3.2 Double Complexes 52
3.3 The Koszul Complex 57
4 Homological Properties of Rings and Modules 64
4.1 Cohen Macaulay and Gorenstein Rings 64
4.2 Dimension 72
4.3 The Acyclicity Lemma 74
4.4 Modules of Finite Projective Dimension 75
4.5 Injective Modules over Noetherian Rings 81
4.6 Dualizing Complexes 86
5 Intersection Multiplicities 93
5.1 Intersection with Divisors 94
v
vi Contents
5.2 The Euler Characteristic of the Koszul Complex 95
5.3 Serre Intersection Multiplicity 105
6 The Homological Conjectures 107
6.1 Conjectures on Intersection Multiplicities 107
6.2 The Peskine Szpiro Intersection Theorem 110
6.3 The Multiplicity Conjectures for Graded Modules 114
7 The Frobenius Map 121
7.1 General Properties of the Frobenius Map 122
7.2 Applications to the Homological Conjectures 122
7.3 Hilbert Kunz Multiplicity and Dutta Multiplicity 125
7.4 Tight Closure 134
7.5 Reduction from Characteristic Zero to Positive
Characteristic 137
Part Two: Chern Classes 139
8 Projective Schemes 141
8.1 Projective Schemes Defined by Z graded Rings 142
8.2 Projective Schemes Denned by Z graded Rings 145
8.3 Hilbert Polynomials and Dimension 151
8.4 Proper Maps 156
8.5 Proper Push Forward of Cycles 157
8.6 Products of Projective Schemes 162
8.7 The Hyperplane Sections on a Projective Scheme 164
8.8 Divisors on Projective Schemes 167
8.9 Commutativity of Intersection with Divisors 170
8.10 Bezout s Theorem 174
9 Chern Classes of Locally Free Sheaves 177
9.1 Sheaves 177
9.2 Chern Classes 180
9.3 Functorial Properties of Chern Classes 187
9.4 Composition of Chern Classes 190
9.5 The Whitney Sum Formula 192
9.6 The Splitting Principle 195
9.7 Chern Characters 196
9.8 Push Forward of Complexes of Sheaves 200
10 The Grassmannian 207
10.1 Local Computations on the Grassmannian 207
Contents vii
10.2 The Canonical Locally Free Sheaves 210
10.3 The Grassmannian of a Locally Free Sheaf 212
10.4 Functorial Properties of the Grassmannian 216
10.5 Computation of Chern Classes via Free Resolutions 220
11 Local Chern Characters 231
11.1 Chern Classes of m primary Matrices 232
11.2 An Example: Multiplicities of m primary Ideals 235
11.3 Cycles Associated to a Complex of Locally Free Sheaves 236
11.4 The Chern Character of a Complex of Locally Free Sheaves 241
11.5 Complexes of Free Modules over a Local Ring 248
11.6 Compatibility with Intersection with Divisors 250
11.7 Composition of Local Chern Characters 253
12 Properties of Local Chern Characters 258
12.1 The Additivity Formula 258
12.2 The Splitting Principle for Complexes 262
12.3 The Multiplicativity Formula 266
12.4 The Todd Class 269
12.5 The Riemann Roch Theorem 274
12.6 The Local Riemann Roch Formula 280
12.7 Local Chern Characters and Dutta Multiplicity 284
13 Applications and Examples 286
13.1 Intersection Multiplicities 286
13.2 Negativity of Intersection Multiplicities 288
13.3 Further Consequences of the Examples 293
13.4 The Intersection Theorem in Mixed Characteristic 295
Bibliography 297
Index 301
|
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author | Roberts, Paul Christopher |
author_facet | Roberts, Paul Christopher |
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dewey-search | 512.24 |
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dewey-tens | 510 - Mathematics |
discipline | Mathematik |
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id | DE-604.BV011858206 |
illustrated | Not Illustrated |
indexdate | 2024-07-09T18:17:33Z |
institution | BVB |
isbn | 0521473160 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008010257 |
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physical | XI, 303 S. |
publishDate | 1998 |
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publisher | Cambridge Univ. Press |
record_format | marc |
series | Cambridge tracts in mathematics |
series2 | Cambridge tracts in mathematics |
spelling | Roberts, Paul Christopher Verfasser aut Multiplicities and chern classes in local algebra Paul C. Roberts 1. publ. Cambridge Cambridge Univ. Press 1998 XI, 303 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 133 Multiplizität Mathematik (DE-588)4200398-2 gnd rswk-swf Chern-Klasse (DE-588)4306750-5 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s Multiplizität Mathematik (DE-588)4200398-2 s DE-604 Chern-Klasse (DE-588)4306750-5 s Cambridge tracts in mathematics 133 (DE-604)BV000000001 133 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008010257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Roberts, Paul Christopher Multiplicities and chern classes in local algebra Cambridge tracts in mathematics Multiplizität Mathematik (DE-588)4200398-2 gnd Chern-Klasse (DE-588)4306750-5 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
subject_GND | (DE-588)4200398-2 (DE-588)4306750-5 (DE-588)4164821-3 |
title | Multiplicities and chern classes in local algebra |
title_auth | Multiplicities and chern classes in local algebra |
title_exact_search | Multiplicities and chern classes in local algebra |
title_full | Multiplicities and chern classes in local algebra Paul C. Roberts |
title_fullStr | Multiplicities and chern classes in local algebra Paul C. Roberts |
title_full_unstemmed | Multiplicities and chern classes in local algebra Paul C. Roberts |
title_short | Multiplicities and chern classes in local algebra |
title_sort | multiplicities and chern classes in local algebra |
topic | Multiplizität Mathematik (DE-588)4200398-2 gnd Chern-Klasse (DE-588)4306750-5 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
topic_facet | Multiplizität Mathematik Chern-Klasse Kommutative Algebra |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008010257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000000001 |
work_keys_str_mv | AT robertspaulchristopher multiplicitiesandchernclassesinlocalalgebra |