WiSe 25/26: Algebraic Geometry I

Lectures: Tuesday 10-12 M103, Wednesday 10-12 M102
Exercises: Thursday 16-18, Friday 12-14 M103

GRIPS page

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 04.11.2025)

Exercises

• Exercise sheet 1 (due 23.10)
• Exercise sheet 2 (due 30.10)
• Exercise sheet 3 (due 06.11)

References

• U. Görtz, T. Wedhorn, Algebraic Geometry I: 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