Teaching in winter semester 2026/2027:
Algebraic Geometry 1
This lecture will be taught in English. It is part of the Master Program.
This lecture will give an introduction to modern algebraic geometry. We will introduce and study the category of schemes, that is to say the notion of "schemes" and "morphisms of schemes" due to A. Grothendieck, and give a lot of examples: affine spaces, projective spaces, etc.... More advanced examples are fiber product of schemes, fibers of a morphism, algebraic vector bundles, groups schemes, etc....
On the way we will have to introduce and recall several concepts and results of commutative algebra and general topology (prime ideals, local rings, noetherian rings and modules, integral closure, sheaf on a topological space, stalk of a sheaf, etc...). We will always aim at giving concrete examples of the notions introduced in the lecture.
This lecture will have a sequel in the next summer semester (2021) where we will further develop the theory of sheaves on schemes through cohomology theory, one of the most powerfull tool of modern algebraic geometry.
It is recommended to have taken the course "Algebra 1 & 2", although not obligatory. However a (very) good knowledge of commutative algebra is required (commutative rings, polynomial rings, localization, modules, tensor product). A good knowledge of basic notions of general topology is also required. And a good knowledge of category theory is very helpful.
References:
A. Grothendieck (et J. Dieudonné), Éléments de Géométrie algébrique, Publications Mathématiques de l' IHES (french)
U. Görtz and T. Wedhorn, Algebraic Geometry: Part I: Schemes. With Examples and Exercises. Springer. (English)
R. Hartshorne, Algebraic Geometry, Springer (English)
Lectures: Tuesday 10:00-12:00 and Thursday 10:00-12:00 in room B132.
First Lecture on Thursday 15th October.
Exercise classes: Tuesday 16:00-18:00 in room B040.
First Exercise class on Tuesday 27th October (the first exercise sheet will be uploaded the week 19th-23rd October).
Tutorial classes (with Andrei Lavrenov): Thursday 12:00-14:00 in room B039.
It will starts either the 22nd or the 29th October, TBA.
Exam: on thursday 4th of February 2027, 10:10-11:50 Room B132.
Exercise Sheets
Category theory
This is a student seminar (for the Bachelor) following the lecture "Category Theory" I gave in the Summer semester 2026. It will start in December. The interested Students should e-mail me to register (Number of talks limited).
Friday 10:00-12:00 (B251). We will meet on Friday 16th October to organize the seminar. The talks will take place at the end of the semester.
References:
S. Mac-Lane, Categories for the working mathematician, Springer
Lina Weitzenböck : (notes of the previous course on category theory) : Script (received July 4)
Retake Exam for Algebra 2 : Friday 23rd October, 10:10-11:50, in B251.
The interested Students should e-mail me to register and to register through LSF when they can. The deadline to register is 15th September.
Previous semesters