Real non-abelian mixed Hodge structures for quasi-projective varieties: formality and splitting
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
September 2016
|
| Series: | Memoirs of the American Mathematical Society
1150 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 178 Seiten |
| ISBN: | 9781470419813 |
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MARC
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| 245 | 1 | 0 | |a Real non-abelian mixed Hodge structures for quasi-projective varieties |b formality and splitting |c J. P. Pridham |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 243, number 1150 (3rd of 4 numbers) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
Structure of the paper 2
Notation 6
Chapter 1. Splittings for MHS on real liomotopy types 7
1.1. The family of formality quasi-isomorphisms 8
1.2. The reduced bar construction 10
1.3. The mixed Hodge structure on Quillen s real liomotopy type and on
liomotopy groups 12
Chapter 2. Non-abelian structures 17
2.1. Hodge filtrations 17
2.2. Twistor filtrations 22
2.3. Mixed Hodge structures 24
2.4. Mixed twistor structures 2(5
2.5. Heal liomotopy types revisited 27
Chapter 3. Structures on cohomology 31
3.1. Cohomology of Hodge filtrations 31
3.2. Cohomology of MHS 32
3.3. Real Deligtie cohomology 32
3.4. Analogies with limit Hodge structures 34
3.5. Archimedean cohomology 34
Chapter 4. Relative Malcev liomotopy types 39
4.1. Review of pro-algebraic liomotopy types 39
4.2. Cosimplicial and DG Hopf algebras 45
4.3. Equivalent formulât ions 49
4.4. The reduced bar construction 56
4.5. Equivalences of liomotopy categories 59
4.6. Families of liomotopy types 62
Chapter 5. Structures on relative Malcev liomotopy types 69
5.1. Homotopy types 69
5.2. Grouplike structures 71
5.3. Splittings over S 73
5.4. Mixed Hodge structures on homotopy groups 74
Chapter 6. MHS 011 relative Malcev homotopy types of compact Kahler
manifolds 79
6.1. Real liomotopy types 79
CONTENTS
G.2. Relative Maleev homotopy types 80
Chapter 7. MTS on relative Maleev homotopy types of compact Kahler
manifolds 87
7.1. Unitary actions 88
Chapter 8. Variations of mixed Hodge and mixed twister structures 93
8.1. Representations in MHS/MTS 93
8.2. Enriching MTS 97
8.3. Absolute Hodge and twistor homotopy types 98
Chapter 9. Monodromy at the Archimedean place 105
9.1. Reformulation via derivations 10G
9.2. Kahler identities 107
9.3. Monodromy calculation 108
Chapter 10. Simplicial and singular varieties 115
10.1. SeniisiiLiple local systems 116
10.2. The Maleev homotopy type 118
10.3. A lived Hodge structures 118
10.4. Enriching twistor structures 120
Chapter 31. Algebraic MHS/MTS for quasi-projective varieties I 123
11.1. The Hodge and twistor filtrations 125
11.2. Higher direct images and residues 126
11.3. Opposedness 127
11.4. Singular and simplicial varieties 130
Chapter 12. Algebraic MHS/ A ITS for quasi-projective variet ies II —
non-trivial monodromy 133
12.1. Constructing mixed Hodge structures 133
12.2. Constructing mixed twistor structures 136
12.3. Unitary monodromy 141
12.4. Singular and simplicial varieties 146
12.5. Alorc general monodromy 147
Chapter 13. Canonical splittings 149
13.1. Splittings of mixed Hodge structures 149
13.2. Splittings of mixed twistor structures 153
13.3. Reduced forms for Hodge and twistor homotopy types 155
Chapter 14. SLo splittings of non-abelian MTS/AIHS and strictification 161
14.1. Simplicial structures 161
14.2. Functors parametrising Hodge and twistor structures 162
14.3. Deformations 163
14.4. Quasi-projeetive varieties 169
Bibliography 175
|
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| id | DE-604.BV043794762 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:35:20Z |
| institution | BVB |
| isbn | 9781470419813 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029205671 |
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| physical | v, 178 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
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| spelling | Pridham, J. P. 1979- Verfasser (DE-588)1112610502 aut Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting J. P. Pridham Providence, Rhode Island American Mathematical Society September 2016 v, 178 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 243, number 1150 (3rd of 4 numbers) Memoirs of the American Mathematical Society 1150 (DE-604)BV008000141 1150 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029205671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pridham, J. P. 1979- Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting Memoirs of the American Mathematical Society |
| title | Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting |
| title_auth | Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting |
| title_exact_search | Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting |
| title_full | Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting J. P. Pridham |
| title_fullStr | Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting J. P. Pridham |
| title_full_unstemmed | Real non-abelian mixed Hodge structures for quasi-projective varieties formality and splitting J. P. Pridham |
| title_short | Real non-abelian mixed Hodge structures for quasi-projective varieties |
| title_sort | real non abelian mixed hodge structures for quasi projective varieties formality and splitting |
| title_sub | formality and splitting |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029205671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT pridhamjp realnonabelianmixedhodgestructuresforquasiprojectivevarietiesformalityandsplitting |