Foundations of Grothendieck duality for diagrams of schemes:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture notes in mathematics
1960 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 478 S. graph. Darst. |
| ISBN: | 9783540854197 ebook 9783540854203 |
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MARC
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| 245 | 1 | 0 | |a Foundations of Grothendieck duality for diagrams of schemes |c Joseph Lipman ; Mitsuyasu Hashimoto |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a X, 478 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1960 | |
| 500 | |a Literaturangaben | ||
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| 650 | 4 | |a Dualité, Principe de (Mathématiques) | |
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| 650 | 4 | |a Théorie des faisceaux | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Duality theory (Mathematics) | |
| 650 | 4 | |a Functor theory | |
| 650 | 4 | |a Schemes (Algebraic geometry) | |
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Record in the Search Index
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| adam_text | Contents
Part I Joseph Lipman: Notes on Derived Functors
and Grothendieck Duality
Abstract 3
Introduction 5
1 Derived and Triangulated Categories 11
1.1 The Homotopy Category K 12
1.2 The Derived Category D 13
1.3 Mapping Cones 15
1.4 Triangulated Categories (A-Categories) 16
1.5 Triangle-Preserving Functors (A-Functors) 25
1.6 A-Subcategories 29
1.7 Localizing Subcategories of K; A-Equivalent Categories 30
1.8 Examples 33
1.9 Complexes with Homology in a Plump Subcategory 35
1.10 Truncation Functors 36
1.11 Bounded Functors; Way-Out Lemma 38
2 Derived Functors 43
2.1 Definition of Derived Functors 43
2.2 Existence of Derived Functors 45
2.3 Right-Derived Functors via Injective Resolutions 52
2.4 Derived Homomorphism Functors 56
2.5 Derived Tensor Product 60
2.6 Adjoint Associativity 65
2.7 Acyclic Objects; Finite-Dimensional Derived Functors 71
3 Derived Direct and Inverse Image 83
3.1 Preliminaries 85
3.2 Adjointness of Derived Direct and Inverse Image 89
vii
viii Contents
3.3 A-Adjoint Functors 97
3.4 Adjoint Functors between Monoidal Categories 101
3.5 Adjoint Functors between Closed Categories 110
3.6 Adjoint Monoidal A-Pseudofunctors 118
3.7 More Formal Consequences: Projection, Base Change 124
3.8 Direct Sums 131
3.9 Concentrated Scheme-Maps 132
3.10 Independent Squares: Kiinneth Isomorphism 144
4 Abstract Grothendieck Duality for Schemes 159
4.1 Global Duality 160
4.2 Sheafified Duality—Preliminary Form 169
4.3 Pseudo-Coherence and Quasi-Properness 171
4.4 Sheafified Duality, Base Change 177
4.5 Proof of Duality and Base Change: Outline 179
4.6 Steps in the Proof 179
4.7 Quasi-Perfect Maps 190
4.8 Two Fundamental Theorems 203
4.9 Perfect Maps of Noetherian Schemes 230
4.10 Appendix: Dualizing Complexes 239
References 253
Index 257
Part II Mitsuyasu Hashimoto: Equivariant Twisted Inverses
Introduction 267
1 Commutativity of Diagrams Constructed
from a Monoidal Pair of Pseudofunctors 271
2 Sheaves on Ringed Sites 287
3 Derived Categories and Derived Functors of Sheaves
on Ringed Sites 311
4 Sheaves over a Diagram of S-Schemes 321
5 The Left and Right Inductions and the Direct
and Inverse Images 327
6 Operations on Sheaves Via the Structure Data 331
7 Quasi-Coherent Sheaves Over a Diagram of Schemes 345
Contents ix
8 Derived Functors of Functors on Sheaves of Modules
Over Diagrams of Schemes 351
9 Simplicial Objects 359
10 Descent Theory 363
11 Local Noetherian Property 371
12 Groupoid of Schemes 375
13 Bokstedt—Neeman Resolutions and HyperExt Sheaves .... 381
14 The Right Adjoint of the Derived Direct Image Functor .. 385
15 Comparison of Local Ext Sheaves 393
16 The Composition of Two Almost-Pseudofunctors 395
17 The Right Adjoint of the Derived Direct Image Functor
of a Morphism of Diagrams 401
18 Commutativity of Twisted Inverse with Restrictions 405
19 Open Immersion Base Change 413
20 The Existence of Compactiflcation and Composition
Data for Diagrams of Schemes Over an Ordered
Finite Category 415
21 Flat Base Change 419
22 Preservation of Quasi-Coherent Cohomology 423
23 Compatibility with Derived Direct Images 425
24 Compatibility with Derived Right Inductions 427
25 Equivariant Grothendieck s Duality 429
26 Morphisms of Finite Flat Dimension 431
27 Cartesian Finite Morphisms 435
28 Cartesian Regular Embeddings and Cartesian
Smooth Morphisms 439
29 Group Schemes Flat of Finite Type 445
30 Compatibility with Derived G-Invariance 449
x Contents
31 Equivariant Dualizing Complexes
and Canonical Modules 451
32 A Generalization of Watanabe s Theorem 457
33 Other Examples of Diagrams of Schemes 463
Glossary 467
References 473
Index 477
Part I
Joseph Lipman: Notes on Derived
Functors and Grothendieck Duality
Abstract 3
Introduction 5
1 Derived and Triangulated Categories 11
1.1 The Homotopy Category K 12
1.2 The Derived Category D 13
1.3 Mapping Cones 15
1.4 Triangulated Categories (A-Categories) 16
1.5 Triangle-Preserving Functors (A-Functors) 25
1.6 A-Subcategories 29
1.7 Localizing Subcategories of K; A-Equivalent Categories 30
1.8 Examples 33
1.9 Complexes with Homology in a Plump Subcategory 35
1.10 Truncation Functors 36
1.11 Bounded Functors; Way-Out Lemma 38
2 Derived Functors 43
2.1 Definition of Derived Functors 43
2.2 Existence of Derived Functors 45
2.3 Right-Derived Functors via Injective Resolutions 52
2.4 Derived Homomorphism Functors 56
2.5 Derived Tensor Product 60
2.6 Adjoint Associativity 65
2.7 Acyclic Objects; Finite-Dimensional Derived Functors 71
3 Derived Direct and Inverse Image 83
3.1 Preliminaries 85
3.2 Adjointness of Derived Direct and Inverse Image 89
3.3 A-Adjoint Functors 97
3.4 Adjoint. Functors between Monoidal Categories 101
3.5 Adjoint Functors between Closed Categories 110
3.6 Adjoint Monoidal A-Pseudofunctors 118
3.7 More Formal Consequences: Projection, Base Change 124
3.8 Direct Sums 131
3.9 Concentrated Scheme-Maps 132
3.10 Independent Squares: Kiinneth Isomorphism 144
1
2 Contents
4 Abstract Grothendieck Duality for Schemes 159
4.1 Global Duality 160
4.2 Sheafified Duality—Preliminary Form 169
4.3 Pseudo-Coherence and Quasi-Properness 171
4.4 Sheafified Duality, Base Change 177
4.5 Proof of Duality and Base Change: Outline 179
4.6 Steps in the Proof 179
4.7 Quasi-Perfect Maps 190
4.8 Two Fundamental Theorems 203
4.9 Perfect Maps of Noetherian Schemes 230
4.10 Appendix: Dualizing Complexes 239
References 253
Index 257
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| language | English |
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| spelling | Foundations of Grothendieck duality for diagrams of schemes Joseph Lipman ; Mitsuyasu Hashimoto Berlin [u.a.] Springer 2009 X, 478 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1960 Literaturangaben Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Schémas (Géométrie algébrique) Théorie des faisceaux Categories (Mathematics) Duality theory (Mathematics) Functor theory Schemes (Algebraic geometry) Sheaf theory Grothendieck-Dualität (DE-588)4158320-6 gnd rswk-swf Schema Mathematik (DE-588)4205720-6 gnd rswk-swf Grothendieck-Dualität (DE-588)4158320-6 s Schema Mathematik (DE-588)4205720-6 s DE-604 Lipman, Joseph 1938- Sonstige (DE-588)122777905 oth Hashimoto, Mitsuyasu Sonstige oth Lecture notes in mathematics 1960 (DE-604)BV000676446 1960 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017139923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Foundations of Grothendieck duality for diagrams of schemes Lecture notes in mathematics Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Schémas (Géométrie algébrique) Théorie des faisceaux Categories (Mathematics) Duality theory (Mathematics) Functor theory Schemes (Algebraic geometry) Sheaf theory Grothendieck-Dualität (DE-588)4158320-6 gnd Schema Mathematik (DE-588)4205720-6 gnd |
| subject_GND | (DE-588)4158320-6 (DE-588)4205720-6 |
| title | Foundations of Grothendieck duality for diagrams of schemes |
| title_auth | Foundations of Grothendieck duality for diagrams of schemes |
| title_exact_search | Foundations of Grothendieck duality for diagrams of schemes |
| title_full | Foundations of Grothendieck duality for diagrams of schemes Joseph Lipman ; Mitsuyasu Hashimoto |
| title_fullStr | Foundations of Grothendieck duality for diagrams of schemes Joseph Lipman ; Mitsuyasu Hashimoto |
| title_full_unstemmed | Foundations of Grothendieck duality for diagrams of schemes Joseph Lipman ; Mitsuyasu Hashimoto |
| title_short | Foundations of Grothendieck duality for diagrams of schemes |
| title_sort | foundations of grothendieck duality for diagrams of schemes |
| topic | Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Schémas (Géométrie algébrique) Théorie des faisceaux Categories (Mathematics) Duality theory (Mathematics) Functor theory Schemes (Algebraic geometry) Sheaf theory Grothendieck-Dualität (DE-588)4158320-6 gnd Schema Mathematik (DE-588)4205720-6 gnd |
| topic_facet | Catégories (Mathématiques) Dualité, Principe de (Mathématiques) Schémas (Géométrie algébrique) Théorie des faisceaux Categories (Mathematics) Duality theory (Mathematics) Functor theory Schemes (Algebraic geometry) Sheaf theory Grothendieck-Dualität Schema Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017139923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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