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Derived Algebraic Geometry : An Elemental Approach.
- Format:
- Book
- Author/Creator:
- Gauthier, Renaud.
- Series:
- De Gruyter Expositions in Mathematics Series
- De Gruyter Expositions in Mathematics Series ; v.75
- Language:
- English
- Physical Description:
- 1 online resource (386 pages)
- Edition:
- 2nd ed.
- Place of Publication:
- Berlin/Boston : Walter de Gruyter GmbH, 2024.
- Summary:
- 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.
- Contents:
- Intro
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 9783111334073
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