Spectral algebraic geometry

Description

Introduction I Fundamentals of Spectral Algebraic Geometry Schemes and Deligne-Mumford Stacks Quasi-Coherent Sheaves Spectral Algebraic Spaces II Proper Morphisms Morphisms of Finite Presentation Proper Morphisms in Spectral Algebraic Geometry Grothendieck Duality Nilpotent, Local, and Complete Modules Formal Spectral Algebraic Geometry III Tannaka Reconstruction and Quasi-Coherent Stacks Tannaka Duality Quasi-Coherent Stacks Smooth and Proper Linear -Categories IV Formal Moduli Problems Deformation Theories: Axiomatic Approach Moduli Problems for Commutative Algebras Moduli Problems for Associative Algebras Moduli Problems for En-Algebras Examples of Formal Moduli Problems V Representability Theorems Deformation Theory and the Cotangent Complex Artin's Representability Theorem Applications of Artin Representability VI Structured Spaces Fractured -Topoi Structure Sheaves Scheme Theory VII Variants of Spectral Algebraic Geometry Derived Differential Topology Derived Complex Analytic Geometry Derived Algebraic Geometry VIII Higher Algebraic Stacks Algebraic Stacks in Derived Algebraic Geometry Artin Representability Coaffine Stacks Generalized Algebraic Gerbes IX Rational and p-adic Homotopy Theory Rational Homotopy Theory p-adic Homotopy Theory Unstable Riemann-Hilbert Correspondence X Appendix Coherent -Topoi Grothendieck Topologies in Commutative Algebra Prestable -Categories Descent for Modules and Linear -Categories Profinite Homotopy Theory