Columbia-Penn Fall 2020 DAG learning seminar

The goal of this seminar is to learn the basics of derived algebraic geometry in detail (this is NOT a survey).
We will meet on Tuesdays at 1:30pm.
We will be following the first 7 lectures (not including lecture 0) of Adeel Khan's notes on descent in algebraic K-theory .
If you would like to participate, contact Roy Magen or Elijah Gunther.
Quick information on presentable categories here.

References:


Talks
Date Speaker Topic Main resource
September 14th 3pm Elijah Gunther Intro to ∞-categories
September 22 1:30pm Svetlana Makarova Intro to stable ∞-categories
September 29 Marielle Ong SCRs Beginning of Lecture 1
October 6 Roy Magen Categories of modules
October 13 Davis Lazowski Descent, fpqc site and its subcanonicity, motivating Barr-Beck
October 20 Cailan Li locally of finite presentation morphisms and open immersions, Zariski covers, derived schemes Lecture 1 (2.7 - 2.10)
October 27 Svetlana Makarova Introduction to QCoh, fpqc descent for QCoh Part 3 of Lecture 1 , part 1 of Lecture 2
November 3 Noah Olander (quasi)-separated and quasi-compact morphisms, base change for qcqs morphisms, compact = perfect for affine schemes Part 2 of Lecture 2
November 10 Roy Magen Thomason-Neeman localization theorem, perfect = compact = dualizable for qcqs schemes, small Zariski site, compact generation of qcoh for qcqs schemes Lecture 3
November 17 Roy Magen Cotangent complex, derivations, deformations Up to part 6 of Lecture 5 (loosely!)
November 24 Marielle Ong End of cotangent complex story, smooth and étale morphisms, total spaces of vector bundles and projective bundles Parts of Lecture 5 and beginning of Lecture 6
December 1 Elijah Gunther