Algebraic Geometry I

Prof. Dr. Sabrina Pauli

Prof. Dr. Timo Richarz

Time and Place

Tuesdays and Fridays, 9:50 – 11:30

Starting: April 22, 2025

Ending: July 25, 2025

Room S215 401 and Zoom (ID: 654 2542 5948, PW: largest six digit number divisible by three)

Exercise session by Aaron Rauchfuß

There are weekly exercise sessions accompanying the lecture.

Mondays, 13:30 – 15:15

Starting: April 28, 2025

Course description

The course is an introduction to basic scheme theory (Schemes, Morphisms, Dimension, Singularities) which lies at the foundation of most areas in modern algebraic geometry and number theory. Some familiarity with commutative algebra is assumed, e.g., as covered in Chapter 1-3 of Introduction to commutative algebra, by M. Atiyah and I. MacDonald. Further tools from commutative algebra are stated (usually without proof) during the lectures whenever we need them. It is recommended to cross read the book of Atiyah-MacDonald. Also it is helpful to know some basic categorical language as in the first paragraphs of Mac Lane’s book, Categories for the Working Mathematician.

Literature

• R. Hartshorne: Algebraic Geometry, Springer GTM 52

• R. Vakil: Foundations of algebraic geometry: Skript (opens in new tab)

• J. de Jong et. al.: The Stacks Project

• U. Goertz, T. Wedhorn: Algebraic Geometry I, Vieweg

• G. Ellingsrud, J. C. Ottem: Introduction to Schemes (opens in new tab)

• A. Grothendieck, J. Dieudonné: Éléments de géométrie algébrique

Notes

• Recollections on Commutative Algebra (opens in new tab)

Recodrings

• You can access the recordings via the Excellence Track in Algebra.