nLab
Spectral Algebraic Geometry

Context

Higher geometry

Higher algebra

This page is to record material related to:

on spectral algebraic geometry.

Contents

  • 0 Introduction

I Fundamentals of Spectral Algebraic Geometry

  • 1 Schemes and Deligne-Mumford Stacks
  • 2 Quasi-Coherent Sheaves
  • 3 Spectral Algebraic Spaces

(see also Structured Spaces)

II Proper Morphisms

  • 4 Morphisms of Finite Presentation
  • 5 Proper Morphisms in Spectral Algebraic Geometry
  • 6 Grothendieck Duality
  • 7 Nilpotent, Local, and Complete Modules
  • 8 Formal Spectral Algebraic Geometry

III Tannaka Reconstruction and Quasi-Coherent Stacks

  • 9 Tannaka Duality
  • 10 Quasi-Coherent Stacks
  • 11 Smooth and Proper Linear \infty-Categories

IV Formal Moduli Problems

  • 12 Deformation Theories: Axiomatic Approach
  • 13 Moduli Problems for Commutative Algebras
  • 14 Moduli Problems for Associative Algebras
  • 15 Moduli Problems for En-Algebras
  • 16 Examples of Formal Moduli Problems

V Representability Theorems

  • 17 Deformation Theory and the Cotangent Complex
  • 18 Artin’s Representability Theorem
  • 19 Applications of Artin Representability

VI Structured Spaces

VII Variants of Spectral Algebraic Geometry

VIII Higher Algebraic Stacks

IX Rational and pp-adic Homotopy Theory

X Appendix

  • A Coherent \infty-Topoi
  • B Grothendieck Topologies in Commutative Algebra
  • C Prestable \infty-Categories
  • D Descent for Modules and Linear \infty-Categories
  • E Profinite Homotopy Theory
category: reference

Last revised on June 11, 2018 at 13:47:46. See the history of this page for a list of all contributions to it.