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401-4146-DRL 2 Credits DR D-MATH
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Derived Algebraic Geometry

Lecturers & Examiners: Dr. Arkadij Bojko
Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-02-05 16:07:26

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)

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance
The exam is only offered in the examination session immediately following the course. In particular, no repetition exam can be offered.

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Derived Algebraic Geometry
  • Tue 16:15-18:00 (CAB G 52)
2 h weekly

Offered In

  • Doctorate Mathematics (More Information at: )
    • Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
      • Graduate School (Official website of the Zurich Graduate School in Mathematics: In addition to the 401-....-DRL course units, adapted versions for doctoral students of the following course units: 263-4400-00L Advanced Graph Algorithms and Optimization 401-3902-21L Network & Integer Optimization: From Theory to Application 401-3904-22L Convex Optimization 401-3629-00L Quantitative Risk Management 401-3652-00L Numerical Methods for Hyperbolic Partial Differential Equations 151-0530-00L Nonlinear Dynamics and Chaos II 227-0434-10L Mathematics of Information 401-4490-22L Topology Optimization of Engineering Systems ... (continued ))