Fiches de cours 2017-2018


Scheme Theory


Lecturer(s) :

Patakfalvi Zsolt
Zdanowicz Maciej Emilian




Only this year


This is a course on the second chapter of the book “Hartshorne: algebraic geometry” treating the foundations of scheme theory. The goal is to build a solid fundation for algebraic geometry by solving all exercises from this chapter.


This is a course on the second chapter of the book 'Hartshorne: algebraic geometry' treating the foundations of scheme theory. The special feature of algebraic geometry is that students have to learn it twice. First, using the 'traditional' or 'classical' point of view, and then using the more general theory of schemes. So, this is a course for those ho have already learned the former and want to learn now the latter.

'Hartshorne: Algebraic Geometry' is the standard foundational graduate textbook for scheme theory. It is famous about the particular approach that the big chunk of the material is in the exercises.

 The goal is to read the material at home, and present all the exercises during the meetings. Each student presents one or more exercises per week. This is a course only for those who have taken a course which is at least equivalent to the alge-braic geometry masters course here at EPFL.

Warning: the course is hard, as the book and the subject is famously hard.  Significant work is needed to be put in at home. There are 128 exercises in the chapter, and these are hard statements, even some theorems are proved in them. We spend about 20 minutes on each exercise 


algebraic geometry, scheme theory

Learning Prerequisites

Required courses

Algebraic geometry (masters course)

Learning Outcomes

By the end of the course, the student must be able to:



Hartshorne: Algebraic Geometry


In the programs

    • Semester
    • Exam form
       Oral presentation
    • Credits
    • Subject examined
      Scheme Theory
    • Lecture
      14 Hour(s)
    • Exercises
      28 Hour(s)
    • Practical work
      14 Hour(s)

Reference week

      Exercise, TP
      Project, other


  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German