The seminar happens weekly on Thursdays, 10:30-11:30am starting from Jan. 15, 2026 at Sieg 227 during the winter quarter. The goal is to understand how derived algebraic geometry can be used in algebraic geometry/topology and number theory. In particular, we are going to try to understand derived Brauer groups, Azumaya algebras etc.
Below are some possible references:
Eugster-Pridham, An introduction to derived (algebraic) geometry, arXiv:2109.14594
Khan, An introduction to derived algebraic geometry, link
Antieau, Derived algebraic geometry (notes from his course), link
Toën, Derived algebraic geometry, arXiv:1401.1044
Lurie, Spectral algebraic geometry, link
Antieau-Gepner, Brauer groups and étale cohomology in derived algebraic geometry, arXiv:1210.0290
Toën, Derived Azumaya algebras and generators for twisted derived categories, arXiv:1002.2599.
Toën-Vaquie, Moduli of objects in dg-categories, arXiv:math/0503269.
Nocera-Pernice, The derived Brauer map via twisted sheaves, arXiv:2205.07789
Ahlqvist-Hekking-Pernice-Savvas, Good moduli spaces for derived algebraic geometry, arXiv:2309.16574
Schedule:
Lecture 1, January 15, 2026: Introduction to DAG, Michele Pernice
Lecture 2, January 22, 2026: Topics TBD, Daniel Rostamloo