Derived Algebraic Geometry

This is a reading group on Derived Algebraic Geometry. We meet at EH 3088 on Tuesdays 4-5:30 pm.

Plan

  1. Introduction.
  2. Basics of Higher Category Theory.
  3. Artin Stacks.
  4. Simplicial Commutative Rings.
  5. Derived Schemes.
  6. (Quasi)coherent sheaves on Derived Schemes.
  7. Derived Formal Schemes.
  8. Derived Artin Stacks.
  9. Formal Deformation Theory.
  10. Derived Artin's representability theorem.
  11. ...

Talks

Talk Speaker Date
Basics of higher category theory IGleb Terentiuk January, 25
Basics of higher category theory II Gleb Terentiuk February, 1
Artin Stacks Riku Kurama February, 8
Dold-Kan CorrespondenceGleb Terentiuk February, 22
Model Structures and Simplicial Commutative Rings Alex Bauman March, 15
Non-Abelian Functors Lukas Scheiwiller March, 22
Derived Schemes Shizhang Li April, 5

References

    Higher Category Theory

  1. Jacob Lurie, Higher Topos Theory.
  2. Jacob Lurie, Higher Algebra.

    Stacks

  3. Angelo Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory.
  4. Martin Olsson, Algebraic Spaces and Stacks.

    Derived Algebraic Geometry

  5. Jacob Lurie, Homotopical Algebraic Geometry II: geometric stacks and applications.
  6. Bertrand Toën Derived Algebraic Geometry.
  7. Dennis Gaisgory, Nick Rozenblyum, A study in derived algebraic geometry.
  8. Jacob Lurie, Spectral Algebraic Geometry, Parts I and II.
  9. Akhil Matthew, Notes on Simplicial Commutative Rings.
  10. Akhil Matthew, Notes on Chapter 1 of HTT.

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