Lecture
Algebraic Geometry II

Algebraic Geometry II: Lecture and Exercise

Prof. Dr. Timo Richarz

This lecture can be attended as part of the Excellence Track in Algebra.

Time and Place

Lecture: Tuesdays, 9:50 – 11:30

Starting: October 14, 2025

Ending: February 13, 2026

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

Exercise session by Vukašin Mihajlović

Exercise sessions will accompany the lecture every two weeks.

Fridays, 9:50 – 11:30

Starting: October 24, 2025

Course Description

This course is the continuation of Algebraic Geometry I. We discuss properties of morphisms of schemes (affine, finite, projective, proper, flat, smooth, étale), derived categories and cohomology of quasi-coherent sheaves, and some applications if time permits. Prerequisites are the language of schemes as covered last term.

• 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 + II, Vieweg

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

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

Exam

This is an oral exam taking place on Thursday, February 19, 2026 in Timo‘s office. Please contact algebra@mathematik.tu-darmstadt.de for a precise time.

Notes

Recordings

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