VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.
Derived Algebraic Geometry
Last Updated: 2026-02-05 16:06:47
Abstract
The main goal is to introduce this subject to a wider audience in a more intuitive way. The course should ideally end with applications of derived algebraic geometry to constructing virtual fundamental classes in enumerative geometry using perverse sheaves.
Objective
A keen listener should understand by the end of the course why derived algebraic geometry is useful and have an idea of where to begin in applying it to problems in enumerative geometry.
Resources
Literature
B. Toën, Derived Algebraic Geometry, arXiv:1401.1044, 2014. J. Lurie. Higher topos theory, Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2009. J. Lurie, On Infinity Topoi, arXiv:math/0306109, 2003. J. Lurie, Derived Algebraic Geometry, Ph.D. thesis, Massachusetts Institute of Technology, Dept. of Mathematics, 2004. B. Toën and G. Vezzosi. Homotopical algebraic geometry I: Topos theory”, Advances in mathematics, 2005. B. Toën and G. Vezzosi, From HAG to DAG: Derived Moduli Stacks:Ax-iomatic, Enriched and Motivic Homotopy Theory, 2004. B. Toën and M. Vaquié, Moduli of objects in dg-categories, Annales scien-tifiques de l’Ecole normale supérieure, 2007. C. Brav, V. Bussi, and D. Joyce, A Darboux theorem for derived schemes with shifted symplectic structure, Journal of the American Mathematical Society, 2019. D. Joyce , P. Safronov, A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes, In Annales de la Faculté des sciences de Toulouse: Mathématiques, 2019. D. Borisov, and D. Joyce, Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds, Geometry & Topology, 2017. K. Tasuki, Virtual classes via vanishing cycles, arXiv:2109.06468, 2021.
Learning Materials (Links)
- Literature
- Derived Algebraic Geometry by B.Töen
- Additional links
- A Darboux theorem for derived schemes with shifted symplectic structure by C. Brav, V. Bussi, and D.
- A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes by D. Joyce , P. Safronov
- From HAG to DAG by B. Toën and G. Vezzosi
- Higher Topos Theory by J.Lurie
- Homotopical algebraic geometry I by B. Toën and G. Vezzosi
- Moduli of objects in dg-categories by B. Toën and M. Vaquié
- On Infinity Topoi
- Virtual classes via vanishing cycles by K. Tasuki
- Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds by D. Borisov, and
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Derived Algebraic Geometry |
|
2 h weekly |
Offered In
-
-
Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
-
-