Homotopy theory of schemes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Providence, R.I.
American Mathematical Society
2006
[Paris] Société Mathématique de France |
| Series: | SMF/AMS texts and monographs
12 Astérisque 256 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 103-104) |
| Physical Description: | VII, 104 S. |
| ISBN: | 9780821831649 082183164X |
Staff View
MARC
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| 100 | 1 | |a Morel, Fabien |d 1965- |e Verfasser |0 (DE-588)132679353 |4 aut | |
| 240 | 1 | 0 | |a Théorie homotopique des schémas |
| 245 | 1 | 0 | |a Homotopy theory of schemes |c Fabien Morel ; translated by James D. Lewis |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2006 | |
| 264 | 1 | |a [Paris] |b Société Mathématique de France | |
| 300 | |a VII, 104 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a SMF/AMS texts and monographs |v 12 | |
| 490 | 1 | |a Astérisque |v 256 | |
| 500 | |a Includes bibliographical references (p. 103-104) | ||
| 650 | 4 | |a Homotopy theory | |
| 650 | 4 | |a K-theory | |
| 650 | 4 | |a Schemes (Algebraic geometry) | |
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Record in the Search Index
| _version_ | 1804137152310673408 |
|---|---|
| adam_text | Contents
1.
Introduction
1
1.1. 1
1.2. Notation,
conventions
and review
3
2.
The homotopic category
6
2.1.
fc-spaces
6
2.2.
The homotopic category
14
2.3.
Base change by a smooth morphism
26
3.
Homotopic excision, homotopic purity
and
projective
blowups
30
3.1.
Mayer-Vietoris property and
Čech
descent
30
3.2.
Homotopic purity
35
3.3.
Projective
blowups
42
4.
Homotopic classification of vector bundles
44
4.1.
Excision properties for the
Picard
group and algebraic K-theory
44
4.2.
Homotopic classification of vector bundles and of GL-torsors
51
4.3.
Higher algebraic X-theory and periodicity
64
4.4.
Homotopy theory over a regular scheme
72
Appendix A: Review of homotopic algebra
74
A.I. Lifting properties
74
A.
2.
Homotopy theory associated to a quasi-simplicial category with
cofibrations and weak equivalences
77
A.3. Homotopic limits and colimits
90
Appendix B: Ample families of invertible bundles on a scheme
100
B.I. Elementary open subsets of a scheme
100
B.2. Schemes admitting an ample family
100
B.3. Smooth fc-schemes and fc-spaces
101
B.4.
Torsors
of Jouanolou-Thomason and
ќ-ѕрасеѕ
101
References
103
|
| adam_txt |
Contents
1.
Introduction
1
1.1. 1
1.2. Notation,
conventions
and review
3
2.
The homotopic category
6
2.1.
fc-spaces
6
2.2.
The homotopic category
14
2.3.
Base change by a smooth morphism
26
3.
Homotopic excision, homotopic purity
and
projective
blowups
30
3.1.
Mayer-Vietoris property and
Čech
descent
30
3.2.
Homotopic purity
35
3.3.
Projective
blowups
42
4.
Homotopic classification of vector bundles
44
4.1.
Excision properties for the
Picard
group and algebraic K-theory
44
4.2.
Homotopic classification of vector bundles and of GL-torsors
51
4.3.
Higher algebraic X-theory and periodicity
64
4.4.
Homotopy theory over a regular scheme
72
Appendix A: Review of homotopic algebra
74
A.I. Lifting properties
74
A.
2.
Homotopy theory associated to a quasi-simplicial category with
cofibrations and weak equivalences
77
A.3. Homotopic limits and colimits
90
Appendix B: Ample families of invertible bundles on a scheme
100
B.I. Elementary open subsets of a scheme
100
B.2. Schemes admitting an ample family
100
B.3. Smooth fc-schemes and fc-spaces
101
B.4.
Torsors
of Jouanolou-Thomason and
ќ-ѕрасеѕ
101
References
103 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Morel, Fabien 1965- |
| author_GND | (DE-588)132679353 |
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| callnumber-first | Q - Science |
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| callnumber-search | QA564 |
| callnumber-sort | QA 3564 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 832 SK 230 SK 240 SK 300 |
| classification_tum | MAT 147f |
| ctrlnum | (OCoLC)69680203 (DE-599)BVBBV022886215 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV022886215 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:52:01Z |
| indexdate | 2024-07-09T21:07:45Z |
| institution | BVB |
| isbn | 9780821831649 082183164X |
| language | English French |
| lccn | 2006047747 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016091125 |
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| physical | VII, 104 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | American Mathematical Society Société Mathématique de France |
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| series | SMF/AMS texts and monographs Astérisque |
| series2 | SMF/AMS texts and monographs Astérisque |
| spelling | Morel, Fabien 1965- Verfasser (DE-588)132679353 aut Théorie homotopique des schémas Homotopy theory of schemes Fabien Morel ; translated by James D. Lewis Providence, R.I. American Mathematical Society 2006 [Paris] Société Mathématique de France VII, 104 S. txt rdacontent n rdamedia nc rdacarrier SMF/AMS texts and monographs 12 Astérisque 256 Includes bibliographical references (p. 103-104) Homotopy theory K-theory Schemes (Algebraic geometry) Schema Mathematik (DE-588)4205720-6 gnd rswk-swf K-Theorie (DE-588)4033335-8 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Schema Mathematik (DE-588)4205720-6 s Homotopietheorie (DE-588)4128142-1 s DE-604 K-Theorie (DE-588)4033335-8 s 1\p DE-604 SMF/AMS texts and monographs 12 (DE-604)BV013184477 12 Astérisque 256 (DE-604)BV002579439 256 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Morel, Fabien 1965- Homotopy theory of schemes SMF/AMS texts and monographs Astérisque Homotopy theory K-theory Schemes (Algebraic geometry) Schema Mathematik (DE-588)4205720-6 gnd K-Theorie (DE-588)4033335-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4205720-6 (DE-588)4033335-8 (DE-588)4128142-1 |
| title | Homotopy theory of schemes |
| title_alt | Théorie homotopique des schémas |
| title_auth | Homotopy theory of schemes |
| title_exact_search | Homotopy theory of schemes |
| title_exact_search_txtP | Homotopy theory of schemes |
| title_full | Homotopy theory of schemes Fabien Morel ; translated by James D. Lewis |
| title_fullStr | Homotopy theory of schemes Fabien Morel ; translated by James D. Lewis |
| title_full_unstemmed | Homotopy theory of schemes Fabien Morel ; translated by James D. Lewis |
| title_short | Homotopy theory of schemes |
| title_sort | homotopy theory of schemes |
| topic | Homotopy theory K-theory Schemes (Algebraic geometry) Schema Mathematik (DE-588)4205720-6 gnd K-Theorie (DE-588)4033335-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopy theory K-theory Schemes (Algebraic geometry) Schema Mathematik K-Theorie Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184477 (DE-604)BV002579439 |
| work_keys_str_mv | AT morelfabien theoriehomotopiquedesschemas AT morelfabien homotopytheoryofschemes |