Filtrations on the homology of algebraic varieties:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1994
|
| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
529 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Volume 110, Number 529 (fourth of 6 numbers) |
| Beschreibung: | IX, 110 S. |
| ISBN: | 0821825917 |
Internformat
MARC
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| 245 | 1 | 0 | |a Filtrations on the homology of algebraic varieties |c Eric M. Friedlander ; Barry Mazur |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1994 | |
| 300 | |a IX, 110 S. | ||
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 529 | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface ix
Introduction 1
Chapter 1. Questions and Speculations 5
1.1. The filiations 5
1.2. Dependence on the projective imbedding 6
1.3. The Strong Lefschetz mapping in Lawson Homology 6
1.4. Equivalence relations on algebraic cycles 7
1.5. Stabilized homotopy of moduli spaces 7
1.6. Joins and Resultants 8
Chapter 2. Abelian monoid varieties 9
2.1. Monoids 9
2.2. Limits 9
2.3. Directed systems attached to an abelian monoid 10
2.4. Limits of covariant functors 11
2.5. Bi algebras 13
2.6. Abelian group completions 14
2.7. Constructing ]ur}H,(M) from H.(M) 16
2.8. Base points 19
2.9. Primitive elements 20
2.10. Mixed Hodge Structure 22
Chapter 3. Chow varieties and Lawson homology 25
3.1. The Chow variety 25
3.2. Functoriality and Chow varieties 26
3.3. Functoriality: algebraic context 32
3.4. The additive monoid 35
3.5. Lawson homology 36
Chapter 4. Correspondences and Lawson homology 39
4.1. Correspondence homomorphisms 39
vi CONTENTS
4.2. The Chow correspondence homomorphism 41
4.3. The Chow correspondence homomorphism and Lawson homology 44
Chapter 5. Multiplication of algebraic cycles 47
5.1. The multiplicative structure on Chow varieties 47
5.2. Bilinear pairings on group completions 50
5.3. The multiplicative structure on Lawson homology 51
5.4. The ring structure on Lawson homology of P° 53
Chapter 6. Operations in Lawson homology 55
6.1. The structure of the algebra A 55
6.2. A geometric description of s 58
6.3. A homological description of iterates of s 58
6.4. The connection between s and the correspondence homomorphism 60
6.5. The operator oj and the Chow correspondence homomorphism 62
6.6. The operator h 63
Chapter 7. Filtrations 67
7.1. The Hodge Filtration 67
7.2. The Geometric filtration 67
7.3. The Topological nitration 68
7.4. The Correspondence subspace 68
7.5. Equality of correspondence and topological filtrations 70
Appendix A. Mixed Hodge Structures, Homology, and Cycle classes 73
A.I. Mixed Hodge Structure on homology and cohomology 73
A.2. Homology and cohomology of smooth varieties 74
A.3. Cycle classes in homology 75
A.4. Change of cycle class under l.c.i. morphisms 76
A.5. Relation to birational change of correspondence 77
A.6. Correspondences and suspensions 78
Appendix B. Trace maps and the Dold Thom Theorem 81
B.I. The inverse image mapping on homology attached to a weighted
map 81
B.2. The Dold Thom theorem 85
Appendix Q. On the group completion of a simplicial monoid 89
Q.I. Rings of fractions 90
Q.2. Grading of flS 1 91
Q.3. The Eilenberg Moore spectral sequence 92
Q.4. A comparison lemma 94
Q.5. Good simplicial monoids 95
Q.6. Homology of the group completion 97
CONTENTS vii
Q.7. Applications to K theory 98
Q.8. A theorem of Mather 102
Q.9. The group completion theorem in Segal s setup 103
References for Appendix Q 105
Bibliography 107
|
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| id | DE-604.BV009788245 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:40:52Z |
| institution | BVB |
| isbn | 0821825917 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006475769 |
| oclc_num | 246281797 |
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| physical | IX, 110 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Friedlander, Eric M. 1944- Verfasser (DE-588)109731867 aut Filtrations on the homology of algebraic varieties Eric M. Friedlander ; Barry Mazur Providence, RI American Math. Soc. 1994 IX, 110 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 529 Volume 110, Number 529 (fourth of 6 numbers) Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd rswk-swf Filter Mathematik (DE-588)4154388-9 gnd rswk-swf Algebraische Mannigfaltigkeit (DE-588)4128509-8 s Filter Mathematik (DE-588)4154388-9 s DE-604 Mazur, Barry 1937- Verfasser (DE-588)107715945 aut American Mathematical Society: Memoirs of the American Mathematical Society 529 (DE-604)BV008000141 529 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006475769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedlander, Eric M. 1944- Mazur, Barry 1937- Filtrations on the homology of algebraic varieties American Mathematical Society: Memoirs of the American Mathematical Society Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Filter Mathematik (DE-588)4154388-9 gnd |
| subject_GND | (DE-588)4128509-8 (DE-588)4154388-9 |
| title | Filtrations on the homology of algebraic varieties |
| title_auth | Filtrations on the homology of algebraic varieties |
| title_exact_search | Filtrations on the homology of algebraic varieties |
| title_full | Filtrations on the homology of algebraic varieties Eric M. Friedlander ; Barry Mazur |
| title_fullStr | Filtrations on the homology of algebraic varieties Eric M. Friedlander ; Barry Mazur |
| title_full_unstemmed | Filtrations on the homology of algebraic varieties Eric M. Friedlander ; Barry Mazur |
| title_short | Filtrations on the homology of algebraic varieties |
| title_sort | filtrations on the homology of algebraic varieties |
| topic | Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Filter Mathematik (DE-588)4154388-9 gnd |
| topic_facet | Algebraische Mannigfaltigkeit Filter Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006475769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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