Algebraic Geometry I - Winter term 2019/20

Dr. Alexander Ivanov

Dr. Alexander Ivanov
Endenicher Allee 60 · Zimmer 1.004
Tel.: 0228-73-3791
E-Mail: ivanov"at"

!!! Exam on March 18 canceled !!!

Due to the situation with the Coronavirus, the exam has to be postponed. According to how things currently stand, the exam will take place before the lectures of the summer term begin. Once a new date for the exam is fixed, it will be announced here. I apologize for any inconvenience.

Time and Place

Monday, 12 (c.t.) - 14h, Kleiner Hörsaal
Thursday, 10 (c.t.) - 12h, Kleiner Hörsaal
First Lecture: Monday 07.10.2019.

Content of the course

This course will cover basic scheme theory.


Commutative algebra (rings, modules, ideals, fields, finiteness, Noetherian and Artinian properties, localization, integral domains, Noether normalization theorem, etc.), some elementary topology. Also some (basic) category theory would be very helpful.


  • R. Hartshorne: Algebraic Geometry GTM 52. Springer.
  • D. Mumford: The Red book of varieties and schemes. Springer LN 1358.
  • R. Vakil: Foundations of algebraic geometry. Online lectures
  • J. de Jong: The Stacks project
  • D. Eisenbud and J. Harris, The Geometry of Schemes, GTM 197, Springer.
  • U. Goertz, T. Wedhorn: Algebraic Geometry I. Vieweg.
  • Q. Liu: Algebraic Geometry and Arithmetic Curves. Oxford GTM
  • A. Grothendieck, J. Dieudonné: Éléments de géométrie algébrique.

See also the notes of the course on algebraic geometry by P. Scholze (typed by Jack Davies)

Exercise sheets

Additional exercises for the lecture are kindly provided by the tutors (Manuel Hoff and Mingjia Zhang). You can find them at the link where X has to be replaced by the number of the current exercise sheet (1,2,3, ... ). Note that solving this exercises does not contribute to the points needed to participate in the final exam.

Exercise sessions

There are weekly exercise sessions accompanying the lecture. It is necessary to attend the exercise sessions and hand in solutions to the exercises in order to participate in the final exam. Please hand in your solutions Monday during the lecture. Registration for the exercise sessions takes place during the first lecture. The regular exercise sessions start in week two.

Group Time and Place Tutor
Group 1 Thuesday 12 (c.t.)-14h, N 0.007 (Neubau) Mingjia Zhang
Group 2 Wednesday 8 (c.t.)-10h, N 0.007 (Neubau) Manuel Hoff
Group 3 Wednesday 16 (c.t.)-18h, 0.006 (main building) Mingjia Zhang/Manuel Hoff


The first written exam will take place on Friday, 14.02.2020 from 9h to 11h in the Großer Hörsaal, Wegelerstraße.
The second written exam will take place on Wednesday, 18.03.2020 from 9h to 11h --- Cancelled: see above. --- in the Kleiner Hösaal, Wegelerstraße.

Last modified: 01.10.2019, Alexander Ivanov