New:
First Exam : On Monday 20th February, from 10:00 to 11:00 the students who wrote the Exam on 09 feb 2023 can come to my office to check their work and grade.
Second Exam : The second exam will take place on 11 April in the room B 004 from 10:00 to 12:00 .
Each student who wants to participate to the second exam has to register by sending me an e-mail before Saturday 4.03.2023.
Algebraic geometry 1.
This lecture (4 hrs) + exercises (2 hrs) will be taught in english in the room A 027 Tuesday, Thursday 10:00-12:00 for the lectures and in the room B 046 (Tuesday 14:00-16:00) for the exercises. The first lecture will be on tuesday 18th October. No exercise class that week.
This lecture will give an introduction to algebraic geometry. We will first introduce and study 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 good knowledge of the classical theory of commutative rings, polynomial rings, and basic notions of general topology is required.
References:
A. Grothendieck (et J. Dieudonné), Éléments de Géométrie algébrique, Publications Mathématiques de l' IHES.
U. Görtz and T. Wedhorn, Algebraic Geometry: Part I: Schemes. With Examples and Exercises. Springer.
R. Hartshorne, Algebraic Geometry, Springer
Exercise sheets .
Previous semesters .