• Bhatt: Algebraization and Tannaka Duality (lots of good results)
• MathOverflow answer
• References:
  • Lurie: Spectral Algebraic Geometry
  • Lurie DAG series:
    • DAG
    • DAG5: Structured Spaces
    • DAG7: Spectral Schemes
    • DAG8: Quasi-Coherent Sheaves and Tannaka Duality Theorems
  • Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi
  • HAG2
  • Book project 'A study in derived algebraic geometry' by D. Gaitsgory and N. Rozenblyum
• Surveys:
  • Rezk on spectral algebraic geometry
  • Toën DAG survey
  • Toën DAG and Deformation Quantization ICM lecture
  • Toën-Vezzosi: From HAG to DAG: derived moduli spaces
  • Vezzosi: What is a derived stack?
  • Gaitsgory: Notes on Geometric Langlands: stacks
  • Lurie: ICM address (deformation theory)
  • Moursund Mathematics Lecture Series. Dr. Jacob Lurie, Lecture 1: “Theory of ‘Spectral’ Algebraic Geometry”
• Seminars:
  • derived algebraic geometry seminar (Penn)
    • Talks
    • Exercises
  • Algebraic K-theory and Derived algebraic geometry
  • derived algebraic geometry seminar
  • Derived Algebraic Geometry Seminar
  • DAG reading group (Fall 2011)
  • Derived Algebraic Geometry seminar (Jerusalem 2010)
  • Graduate Seminar. Geometric Representation theory. Fall 2009--Spring 2010
• Courses, lecture notes, etc:
  • Adeel Khan's lecture notes:
    • Descent in algebraic K-theory 2017/2018
    • Grothendieck-Riemann-Roch theorem 2018
    • Descent in algebraic K-theory 2020
  • Minicourse by Rok Gregoric
  • Pieter Belmans on the topos of derived stacks at Derived Algebraic Geometry Winter School 2013
  • Minicurso de geometría algebraica derivada
  • Talks by Benjamin Antieau at MSRI " Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces"
  • Paul Goerss Topological Algebraic Geometry (slides)
  • Toën stuff