∞-Categories in Algebraic Geometry

Spring 2022

Koszul duality patterns have influenced several recent developments in algebraic geometry, ranging from the classification of formal deformations by Lie algebras and the unobstructedness of Calabi-Yau varieties to purely inseparable Galois theory and derived Galois deformation rings. In this class, we will explain some of these results and review the required ∞-categorical background.

General Information

Time / place: Thursdays 10-12 in salle 1A8 (Orsay).
Contact: lukas.brantner@universite-paris-saclay.fr

Lecture notes

Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9

Student presentations
Schlessinger Theorem (Alexandre Guillemot)
Lurie's derived Schlessinger theorem (Elio Pivet)
The proof of the derived Schlessinger theorem (Yuanyang Jiang)
Comonadicity and descent (Yuchen Wu)