Derived Algebraic Geometry : : An Elemental Approach / / Renaud Gauthier.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2024 Part 1
• VerfasserIn: Gauthier, Renaud,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2024]; ©2024
• Year of Publication: 2024
• Edition: 2nd Edition
• Language: English
• Series: De Gruyter Expositions in Mathematics , 75
• Physical Description: 1 online resource (XXII, 364 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783111334073; 9783111332192
• ISSN: 0938-6572
• DOI: 10.1515/9783111334073
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: 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 chapter on Derived Motivic Spectrais now included as is an extended introduction to Infinity Category as well as a revised chapter on Stacks.