Derived Algebraic Geometry : : An Elemental Approach / / Renaud Gauthier.
The second edition presents schemes, simplicial sets, higher categories, model categories, derived algebraic geometry, and spectral algebraic geometry in a self-contained manner. It discusses Motives, Goodwillie Calculus, Higher Galois, Supersymmetry, and topics in physical mathematics. A new chapte...
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2024] ©2024 |
| Year of Publication: | 2024 |
| Edition: | 2nd Edition |
| Language: | English |
| Series: | De Gruyter Expositions in Mathematics ,
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| Physical Description: | 1 online resource (XXII, 364 p.) |
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Gauthier, Renaud, author. aut http://id.loc.gov/vocabulary/relators/aut Derived Algebraic Geometry : An Elemental Approach / Renaud Gauthier. 2nd Edition Berlin ; Boston : De Gruyter, [2024] ©2024 1 online resource (XXII, 364 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 75 Frontmatter -- Preface to the second edition -- Introduction -- Contents -- Part I: Prerequisites -- 1 Schemes -- 2 Simplicial sets -- 3 ∞-categories -- 4 Model categories -- Part II: Derived algebraic geometry -- 5 Introduction -- 6 Stacks on simplicial sites -- 7 Stacks on model sites -- 8 Stacks on Segal sites -- 9 Application: étale derived stacks -- Part III: Spectral algebraic geometry -- 10 Introduction -- 11 ∞-operads -- 12 Spectra -- 13 E∞-ring spectra -- 14 Spectral Deligne–Mumford stacks -- 15 Spectral Artin representability -- 16 Representation theory of formal moduli problems -- 17 Relations between quasi-coherent sheaves -- Part IV: Applications -- 18 A dual representation in spectral algebraic geometry -- 19 A Connection SAG-DAG -- 20 Motifs in DAG -- 21 Introduction to a category of derived motivic spectra -- 22 Goodwillie calculus and geometric stacks -- 23 Spectral “schematization” of homotopy types -- 24 Higher Galois for Segal topos -- 25 Infinity-topoi and natural phenomena: generation -- 26 Segal topoi and the universality of physical laws -- 27 Internal Bousfield localizations -- 28 Supersymmetric derived stacks -- 29 Taking stock – Physical Mathematics -- Bibliography -- Index -- Notations restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The second edition presents schemes, simplicial sets, higher categories, model categories, derived algebraic geometry, and spectral algebraic geometry in a self-contained manner. It discusses Motives, Goodwillie Calculus, Higher Galois, Supersymmetry, and topics in physical mathematics. A new chapter on Derived Motivic Spectrais now included as is an extended introduction to Infinity Category as well as a revised chapter on Stacks. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Mrz 2024) Höhere Topoi. Modellkategorie. Segal Topoi. Stacks. Unendlich-Kategorie. MATHEMATICS / Algebra / General. bisacsh Stacks, Infinity Categories, Model Categories, Higher topoi, Segal topoi. Title is part of eBook package: De Gruyter DG Plus DeG Package 2024 Part 1 9783111332192 EPUB 9783111334219 print 9783111333663 https://doi.org/10.1515/9783111334073 https://www.degruyter.com/isbn/9783111334073 Cover https://www.degruyter.com/document/cover/isbn/9783111334073/original |
| language |
English |
| format |
eBook |
| author |
Gauthier, Renaud, Gauthier, Renaud, |
| spellingShingle |
Gauthier, Renaud, Gauthier, Renaud, Derived Algebraic Geometry : An Elemental Approach / De Gruyter Expositions in Mathematics , Frontmatter -- Preface to the second edition -- Introduction -- Contents -- Part I: Prerequisites -- 1 Schemes -- 2 Simplicial sets -- 3 ∞-categories -- 4 Model categories -- Part II: Derived algebraic geometry -- 5 Introduction -- 6 Stacks on simplicial sites -- 7 Stacks on model sites -- 8 Stacks on Segal sites -- 9 Application: étale derived stacks -- Part III: Spectral algebraic geometry -- 10 Introduction -- 11 ∞-operads -- 12 Spectra -- 13 E∞-ring spectra -- 14 Spectral Deligne–Mumford stacks -- 15 Spectral Artin representability -- 16 Representation theory of formal moduli problems -- 17 Relations between quasi-coherent sheaves -- Part IV: Applications -- 18 A dual representation in spectral algebraic geometry -- 19 A Connection SAG-DAG -- 20 Motifs in DAG -- 21 Introduction to a category of derived motivic spectra -- 22 Goodwillie calculus and geometric stacks -- 23 Spectral “schematization” of homotopy types -- 24 Higher Galois for Segal topos -- 25 Infinity-topoi and natural phenomena: generation -- 26 Segal topoi and the universality of physical laws -- 27 Internal Bousfield localizations -- 28 Supersymmetric derived stacks -- 29 Taking stock – Physical Mathematics -- Bibliography -- Index -- Notations |
| author_facet |
Gauthier, Renaud, Gauthier, Renaud, |
| author_variant |
r g rg r g rg |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Gauthier, Renaud, |
| title |
Derived Algebraic Geometry : An Elemental Approach / |
| title_sub |
An Elemental Approach / |
| title_full |
Derived Algebraic Geometry : An Elemental Approach / Renaud Gauthier. |
| title_fullStr |
Derived Algebraic Geometry : An Elemental Approach / Renaud Gauthier. |
| title_full_unstemmed |
Derived Algebraic Geometry : An Elemental Approach / Renaud Gauthier. |
| title_auth |
Derived Algebraic Geometry : An Elemental Approach / |
| title_alt |
Frontmatter -- Preface to the second edition -- Introduction -- Contents -- Part I: Prerequisites -- 1 Schemes -- 2 Simplicial sets -- 3 ∞-categories -- 4 Model categories -- Part II: Derived algebraic geometry -- 5 Introduction -- 6 Stacks on simplicial sites -- 7 Stacks on model sites -- 8 Stacks on Segal sites -- 9 Application: étale derived stacks -- Part III: Spectral algebraic geometry -- 10 Introduction -- 11 ∞-operads -- 12 Spectra -- 13 E∞-ring spectra -- 14 Spectral Deligne–Mumford stacks -- 15 Spectral Artin representability -- 16 Representation theory of formal moduli problems -- 17 Relations between quasi-coherent sheaves -- Part IV: Applications -- 18 A dual representation in spectral algebraic geometry -- 19 A Connection SAG-DAG -- 20 Motifs in DAG -- 21 Introduction to a category of derived motivic spectra -- 22 Goodwillie calculus and geometric stacks -- 23 Spectral “schematization” of homotopy types -- 24 Higher Galois for Segal topos -- 25 Infinity-topoi and natural phenomena: generation -- 26 Segal topoi and the universality of physical laws -- 27 Internal Bousfield localizations -- 28 Supersymmetric derived stacks -- 29 Taking stock – Physical Mathematics -- Bibliography -- Index -- Notations |
| title_new |
Derived Algebraic Geometry : |
| title_sort |
derived algebraic geometry : an elemental approach / |
| series |
De Gruyter Expositions in Mathematics , |
| series2 |
De Gruyter Expositions in Mathematics , |
| publisher |
De Gruyter, |
| publishDate |
2024 |
| physical |
1 online resource (XXII, 364 p.) Issued also in print. |
| edition |
2nd Edition |
| contents |
Frontmatter -- Preface to the second edition -- Introduction -- Contents -- Part I: Prerequisites -- 1 Schemes -- 2 Simplicial sets -- 3 ∞-categories -- 4 Model categories -- Part II: Derived algebraic geometry -- 5 Introduction -- 6 Stacks on simplicial sites -- 7 Stacks on model sites -- 8 Stacks on Segal sites -- 9 Application: étale derived stacks -- Part III: Spectral algebraic geometry -- 10 Introduction -- 11 ∞-operads -- 12 Spectra -- 13 E∞-ring spectra -- 14 Spectral Deligne–Mumford stacks -- 15 Spectral Artin representability -- 16 Representation theory of formal moduli problems -- 17 Relations between quasi-coherent sheaves -- Part IV: Applications -- 18 A dual representation in spectral algebraic geometry -- 19 A Connection SAG-DAG -- 20 Motifs in DAG -- 21 Introduction to a category of derived motivic spectra -- 22 Goodwillie calculus and geometric stacks -- 23 Spectral “schematization” of homotopy types -- 24 Higher Galois for Segal topos -- 25 Infinity-topoi and natural phenomena: generation -- 26 Segal topoi and the universality of physical laws -- 27 Internal Bousfield localizations -- 28 Supersymmetric derived stacks -- 29 Taking stock – Physical Mathematics -- Bibliography -- Index -- Notations |
| isbn |
9783111334073 9783111332192 9783111334219 9783111333663 |
| issn |
0938-6572 ; |
| url |
https://doi.org/10.1515/9783111334073 https://www.degruyter.com/isbn/9783111334073 https://www.degruyter.com/document/cover/isbn/9783111334073/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
516 - Geometry |
| dewey-full |
516.35 |
| dewey-sort |
3516.35 |
| dewey-raw |
516.35 |
| dewey-search |
516.35 |
| doi_str_mv |
10.1515/9783111334073 |
| oclc_num |
1415894802 |
| work_keys_str_mv |
AT gauthierrenaud derivedalgebraicgeometryanelementalapproach |
| status_str |
n |
| ids_txt_mv |
(DE-B1597)663730 (OCoLC)1415894802 |
| carrierType_str_mv |
cr |
| hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2024 Part 1 |
| is_hierarchy_title |
Derived Algebraic Geometry : An Elemental Approach / |
| container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2024 Part 1 |
| _version_ |
1806144939717820417 |
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