Residues and duality: lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1966
|
| Series: | Lecture notes in mathematics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 423 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Residues and duality |b lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 |c Robin Hartshorne |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1966 | |
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| 490 | 1 | |a Lecture notes in mathematics |v 20 | |
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Record in the Search Index
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| adam_text | CONTENTS
page
Preface III
Contents VI
Introduction 1
Chapter I. The Derived Category 19
§O. Introduction 19
§1. Triangulated categories 20
82. K(A) is triangulated 25
§3. Localization of categories 28
§4. Qis and the derived category 35
§5. Derived functors 49
§6. Examples. Ext and R Horn* 62
§7. Way-out functors and isomorphisms 68
Chapter II. Application to Preschemes 85
8l. Categories of sheaves 85
§2. The derived functors of f# and T 87
63. The derived functor of Horn* 9O
§4. The derived functors of ® and f* 93
§5. Relations among the derived functors 100
§6. Compatibilities among the relations of §5 115
§7. Injective sheaves on a locally noetherian
prescheme 120
Chapter III. Duality for Projective Morphisms 137
§1. Differentials 137
§2. f* for a smooth morphism f * 145
S3. Recall of the explicit calculations 148
84. The trace map for projective space 154
85. The duality theorem for projective space 160
86. Duality for a finite morphism 164
§7. The fundamental local isomorphism 176
88. f* for embeddable morphisms 184
89. The residue symbol 195
§10. Trace for projective morphisms 200
Sll. Duality for projective morphisms 210
page
Chapter IV. Local Cohomology 215
§1. Local cohomology groups, sheaves, and complexes 215
§2. Depth and the Cousin complex 229
S3. Generalization to complexes 240
Chapter V. Dualizing Complexes and Local Duality 252
§0. Introduction 252
Si. Example: duality for abelian groups 254
§2. Dualizing complexes 257
S3. Uniqueness of the dualizing complex 266
84. Local cohomology on a prescheme 272
85. Dualizing functors on a local noetherian ring 275
86. Local duality 276
87. Application to dualizing complexes 282
88. Pointwise dualizing complexes and f* 286
89. Gorenstein preschemes 293
§10. Existence of dualizing complexes 299
Chapter VI. Residual Complexes 302
80. Introduction 302
81. Residual complexes 304
§2. Functorial properties 311
§3. f for residual complexes 318
§4. Trace for residual complexes 335
85. Behavior with respect to certain base changes 349
Chapter VII. The Duality Theorem 357
§1. Curves over an Artin ring 357
82. The residue theorem 369
S3. The duality theorem for proper morphisms 374
§4. Smooth morphisms 388
Index of Definitions 394
Index of Notations 396
Bibliography 401
Appendix. Cohomologie a Support Propre, et Construction du
Foncteur f!, par P. Deligne 404
Errata 422
|
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| spelling | Hartshorne, Robin 1938- Verfasser (DE-588)133225089 aut Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 Robin Hartshorne Berlin [u.a.] Springer 1966 423 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 20 Grothendieck, A (Alexandre) Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Faisceaux, Théorie des Homologie Categories (Mathematics) Homology theory Sheaf theory Residuum (DE-588)4271170-8 gnd rswk-swf Qualität (DE-588)4047966-3 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Residuum (DE-588)4271170-8 s Dualität (DE-588)4013161-0 s DE-604 Qualität (DE-588)4047966-3 s Lecture notes in mathematics 20 (DE-604)BV000676446 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001837941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hartshorne, Robin 1938- Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 Lecture notes in mathematics Grothendieck, A (Alexandre) Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Faisceaux, Théorie des Homologie Categories (Mathematics) Homology theory Sheaf theory Residuum (DE-588)4271170-8 gnd Qualität (DE-588)4047966-3 gnd Dualität (DE-588)4013161-0 gnd |
| subject_GND | (DE-588)4271170-8 (DE-588)4047966-3 (DE-588)4013161-0 (DE-588)1071861417 |
| title | Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 |
| title_auth | Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 |
| title_exact_search | Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 |
| title_full | Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 Robin Hartshorne |
| title_fullStr | Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 Robin Hartshorne |
| title_full_unstemmed | Residues and duality lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 Robin Hartshorne |
| title_short | Residues and duality |
| title_sort | residues and duality lecture notes of a seminar on the work of a grothendieck given at harvard 1963 64 |
| title_sub | lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64 |
| topic | Grothendieck, A (Alexandre) Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Faisceaux, Théorie des Homologie Categories (Mathematics) Homology theory Sheaf theory Residuum (DE-588)4271170-8 gnd Qualität (DE-588)4047966-3 gnd Dualität (DE-588)4013161-0 gnd |
| topic_facet | Grothendieck, A (Alexandre) Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Faisceaux, Théorie des Homologie Categories (Mathematics) Homology theory Sheaf theory Residuum Qualität Dualität Konferenzschrift |
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