Derived Algebraic Geometry
An Elemental Approach
2nd Edition
Published on 29. January 2024
XXII, 364 pages
978-3-11-133407-3 (ISBN)
Description
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.
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01/2024
2nd Edition
De Gruyter
€134.95
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01/2024
2nd Edition
De Gruyter
€144.95
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Person
Renaud Gauthier , University of Mary, USA.
Content
- Intro
- Preface to the second edition
- Introduction
- Contents
- Part I: Prerequisites
- 1 Schemes
- 2 Simplicial sets
- 3 8-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 8-operads
- 12 Spectra
- 13 E8-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
