Derived Algebraic Geometry Reading Group 2020

This is a reading group on derived algebraic geometry. The ultimate goal is to go through Lurie's thesis and understand how to work with ``derived'' objects.

The seminar meets on Fridays 9am--10:30am SF time (12pm-1:30pm NY time, 7pm-8:30pm Moscow time) on zoom.

Schedule

Summer Term
1 June 24 Bogdan Z. Introduction
2 June 26 Arpon R. Basics of ∞-categories
3 July 3 Sasha P. Simplicial Commutative Rings I. Main definitions and the Sym functor
4 July 10 Kirill M. Simplicial Commutative Rings II. Cotangent Complex and Square Zero Extensions
5 July 17 Kirill M. Simplicial Commutative Rings III. Flat, Etale and Smooth Morphisms
6 July 24 Arpon R. ∞-topoi
7 July 31 Sean C. Derived Schemes
8 Aug. 7 Lie Q. Quasi-Coherent and Coherent Sheaves on Derived Schemes
9 Aug. 14 Bogdan Z. Derived Formal Schemes. Formal GAGA
10 Aug. 21 Mitya K. Derived Artin Stacks
11 Aug. 28 Bogdan Z. Derived Artin Representability Theorem

Here are some references relevant to this seminar:

Classical Stuff

[Q1] Homotopical Algebra, Daniel Quillen.
[Q2] On the (co)homology of commutative rings, Daniel Quillen.
[Q3] Homology of commutative rings, Daniel Quillen.
[GJ] Simplicial Homotopy Theory, Paul Goerss and John Jardine.

∞-categories

[HTT] Higher Topos Theory, Jacob Lurie.
[L2] On ∞-topoi, Jacob Lurie.
[A1] Notes On Chapter 1 Of HTT, Akhil's notes.

Derived Algebraic Geometry

[L] Derived Algebraic Geometry, Jacob Lurie's Thesis.
[DAG V] Derived Algebraic Geometry V: Structured Spaces, Jacob Lurie.
[A2] Simplicial Commutative Rings, Akhil's notes.
[SAG] Spectral Algebraic Geometry (Section 25), Jacob Lurie.

Exercises

Problem Set 1, from 2010 DAG seminar at Jerusalem
Problem Set 2, from 2010 DAG seminar at Jerusalem
Problem Set 3, from 2010 DAG seminar at Jerusalem
Problem Set 4, from 2010 DAG seminar at Jerusalem