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...
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| Online Access: |
Full Text (via ProQuest) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; Boston :
Walter de Gruyter GmbH,
[2024]
|
| Edition: | 2nd edition. |
| Series: | De Gruyter expositions in mathematics ;
75. |
| Subjects: |
Table of 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.