WiSe 25/26: Algebraic Geometry I
Lectures: Tuesday 10-12 M103, Wednesday 10-12 M102
Exercises: Thursday 16-18, Friday 12-14 M103
This course covers the foundations of algebraic geometry, which is the study of geometric objects defined by polynomial equations and plays a central role in modern mathematics. We will introduce the fundamental notion of scheme and study its properties.
This course is fundamental for all students who plan to specialize in the direction of Arithmetic Geometry (MArGeo). It will continue in the summer term as Algebraic Geometry II.
Lecture notes
The lecture notes contain all the material from the lecture, without the proofs.
Lecture notes (updated on 05.02.2025)
Exercises
- Sheet 1 (due 23.10)
- Sheet 2 (due 30.10)
- Sheet 3 (due 06.11)
- Sheet 4 (due 13.11)
- Sheet 5 (due 20.11)
- Sheet 6 (due 27.11)
- Sheet 7 (due 04.12)
- Sheet 8 (due 11.12)
- Sheet 9 (due 18.12)
- Sheet 10 (due 08.01)
- Sheet 11 (due 15.01)
- Sheet 12 (due 22.01)
- Sheet 13 (due 29.01)
- Sheet 14 (due 05.02)
References
- U. Görtz, T. Wedhorn, Algebraic Geometry I: Schemes, Springer Link, 2020
- D. Eisenbud, J. Harris, The Geometry of Schemes, Springer Link, 2020
- Yu. I. Manin, Introduction to the Theory of Schemes, Springer Link, 2018
- R. Hartshorne, Algebraic Geometry, Springer Link, 1977
- R. Vakil, The Rising Sea: Foundations of Algebraic Geometry, 2024