Six lectures on commutative algebra: [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra]
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1998
|
| Schriftenreihe: | Progress in mathematics
166 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 398 S. |
| ISBN: | 376435951X 081765951X |
Internformat
MARC
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| 245 | 1 | 0 | |a Six lectures on commutative algebra |b [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] |c J. Elias ... ed. |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1998 | |
| 300 | |a IX, 398 S. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 166 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xi
Luchezar L. Avramov
Infinite Free Resolutions
Introduction 1
1 Complexes 4
1.1 Basic constructions 4
1.2 Syzygies 7
1.3 Differential graded algebra 10
2 Multiplicative Structures on Resolutions 14
2.1 DG algebra resolutions 14
2.2 DG module resolutions 18
2.3 Products versus minimality 21
3 Change of Rings 24
3.1 Universal resolutions 24
3.2 Spectral sequences 29
3.3 Upper bounds 31
4 Growth of Resolutions 34
4.1 Regular presentations 34
4.2 Complexity and curvature 38
4.3 Growth problems 41
5 Modules over Golod Rings 44
5.1 Hypersurfaces 44
5.2 Golod rings 46
5.3 Golod modules 50
6 Tate Resolutions 53
6.1 Construction 54
6.2 Derivations 58
6.3 Acyclic closures 61
vi Contents
7 Deviations of a Local Ring 64
7.1 Deviations and Betti numbers 65
7.2 Minimal models 66
7.3 Complete intersections 71
7.4 Localization 72
8 Test Modules 75
8.1 Residue field 75
8.2 Residue domains 77
8.3 Conormal modules 83
9 Modules over Complete Intersections 87
9.1 Cohomology operators 87
9.2 Betti numbers 92
9.3 Complexity and Tor 95
10 Homotopy Lie Algebra of a Local Ring 99
10.1 Products in cohomology 100
10.2 Homotopy Lie algebra 103
10.3 Applications 106
References 110
Mark L. Green
Generic Initial Ideals
Introduction 119
1 The Initial Ideal 120
2 Regularity and Saturation 137
3 The Macaulay Gotzmann Estimates on the Growth of Ideals 147
4 Points in P2 and Curves in P3 157
5 Gins in the Exterior Algebra 172
6 Lexicographic Gins and Partial Elimination Ideals 177
References 185
Craig Huneke
Tight Closure, Parameter Ideals, and Geometry
Foreword 187
1 An Introduction to Tight Closure 187
2 How Does Tight Closure Arise? 193
3 The Test Ideal I 200
Contents vii
4 The Test Ideal II: the Gorenstein Case 205
5 The Tight Closure of Parameter Ideals 210
6 The Strong Vanishing Theorem 215
7 Plus Closure 219
8 F Rational Rings 222
9 Rational Singularities 225
10 The Kodaira Vanishing Theorem 228
References 231
Peter Schenzel
On the Use of Local Cohomology in Algebra and Geometry
Introduction 241
1 A Guide to Duality 243
1.1 Local Duality 243
1.2 Dualizing Complexes and Some Vanishing Theorems 249
1.3 Cohomological Annihilators 256
2 A Few Applications of Local Cohomology 259
2.1 On Ideal Topologies 259
2.2 On Ideal Transforms 263
2.3 Asymptotic Prime Divisors 265
2.4 The Lichtenbaum Hartshorne Vanishing Theorem 272
2.5 Connectedness Results 273
3 Local Cohomology and Syzygies 276
3.1 Local Cohomology and Tor s 276
3.2 Estimates of Betti Numbers 281
3.3 Castelnuovo Mumford Regularity 282
3.4 The Local Green Modules 286
References 290
Giuseppe Valla
Problems and Results on Hilbert Functions of Graded Algebras
Introduction 293
1 Macaulay s Theorem 296
2 The Perfect Codimension Two and Gorenstein
Codimension Three Case 301
3 The EGH Conjecture 311
viii Contents
4 Hilbert Function of Generic Algebras 317
5 Fat Points: Waring s Problem and Symplectic Packing 319
6 The HF of a CM Local Ring 329
References 341
Wolmer V. Vasconcelos
Cohomological Degrees of Graded Modules
Introduction 345
1 Arithmetic Degree of a Module 349
Multiplicity 349
Castelnuovo Mumford regularity 350
Arithmetic degree of a module 351
Stanley Reisner rings 352
Computation of the arithmetic degree of a module 353
Degrees and hyperplane sections 354
Arithmetic degree and hyperplane sections 354
2 Reduction Number of an Algebra 357
Castelnuovo Mumford regularity and reduction number 357
Hilbert function and the reduction number of an algebra 358
The relation type of an algebra 359
Cayley Hamilton theorem 360
The arithmetic degree of an algebra versus its reduction number 361
Reduction equations from integrality equations 363
3 Cohomological Degree of a Module 364
Big degs 364
Dimension one 365
Homological degree of a module 365
Dimension two 366
Hyperplane section 367
Generalized Cohen Macaulay modules 370
Homologically associated primes of a module 371
Homological degree and hyperplane sections 372
Homological multiplicity of a local ring 376
4 Regularity versus Cohomological Degrees 377
Castelnuovo regularity 378
5 Cohomological Degrees and Numbers of Generators 380
Contents ix
6 Hilbert Functions of Local Rings 381
Bounding rules 382
Maximal Hilbert functions 383
Gorenstein ideals 385
General local rings 385
Bounding reduction numbers 386
Primary ideals 387
Depth conditions 388
7 Open Questions 389
Bounds problems 389
Cohomological degrees problems 390
References 390
Index 393
|
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| genre_facet | Konferenzschrift 1996 Barcelona |
| id | DE-604.BV011907115 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:18:21Z |
| institution | BVB |
| isbn | 376435951X 081765951X |
| language | English |
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| physical | IX, 398 S. |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] J. Elias ... ed. Boston [u.a.] Birkhäuser 1998 IX, 398 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 166 Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1996 Barcelona gnd-content Kommutative Algebra (DE-588)4164821-3 s DE-604 Elias, Juan Sonstige oth Progress in mathematics 166 (DE-604)BV000004120 166 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008047313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] Progress in mathematics Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)1071861417 |
| title | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] |
| title_auth | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] |
| title_exact_search | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] |
| title_full | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] J. Elias ... ed. |
| title_fullStr | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] J. Elias ... ed. |
| title_full_unstemmed | Six lectures on commutative algebra [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] J. Elias ... ed. |
| title_short | Six lectures on commutative algebra |
| title_sort | six lectures on commutative algebra summer school on commutative algebra held from july 16 to 26 1996 at the centre de recerca matematica crm in bellaterra |
| title_sub | [Summer School on Commutative Algebra, held from July 16 to 26, 1996 at the Centre de Recerca Matemàtica (CRM) in Bellaterra] |
| topic | Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Kommutative Algebra Konferenzschrift 1996 Barcelona |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008047313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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