Advanced Algebraic Geometry, Universiteit Leiden, Fall 2013



Bas Edixhoven and David Holmes.

Time and place

Tuesdays, lecture 15:45--17:30, problem session 14:45--15:30, all in room 401.

Course outline

The aim of this course is to state the Grothendieck Hirzebruch Riemann Roch theorem for morphisms of smooth projective varieties over a field, and prove as much of it as we can. This also means that the necessary tools will be introduced:

Once we have these tools available, the general Grothendieck Hirzebruch Riemann Roch theorem is easily stated. We follow the article by Borel and Serre (see the list of references below).

In the remaining two weeks we will try to present as much as possible of the proof given in Borel-Serre:


Le théorème de Riemann Roch
Algebraic geometry. Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977.
de Jong et al.
Stacks project.

Lecture notes

For David's notes, go to his home page.


Here is the take home assigment. Note that we want to receive the solutions by Sunday January 26, 23:59. We will inform the students who registered for the oral exams on January 28 en 29 about the schedule.
Bas Edixhoven <>
Last modified: Tue Dec 10 17:52:33 CET 2013