NMAK16000U Algebraic Geometry 2 (AlgGeo2)

Volume 2026/2027
Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

Content

This course is an introduction to scheme theory. We will cover affine schemes, gluing for general schemes, local and global properties of schemes, and morphisms of schemes, quasicoherent sheaves on schemes, and their cohomology with applications to curves.

Learning Outcome

Knowledge: To display an understanding of the course topics and contents at a level suitable for further studies in Algebraic Geometry.

Skills: At the end of the course, the student is expected to be able to follow and reproduce arguments at a high level of abstraction corresponding to the course contents. 

Competences: At the end of the course, the student is expected to be able to apply basic techniques and results to concrete examples.

Course notes

It is recommended that the students have taken the courses Algebraic Geometry (AlgGeo), Homological Algebra (HomAlg) and Commutative Algebra (KomAlg).
Students should also have some knowledge about category theory.
Academic qualifications equivalent to a BSc degree are recommended.
4 hours lectures and 4 hours exercises per week for 9 weeks.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 134
  • Theory exercises
  • 36
  • Total
  • 206
Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Weekly homework accounting for 50% of the grade and a three-hour 'closed-book' final in-class problem set accounting for 50% of the grade
Aid
Only certain aids allowed (see description below)

Weekly homework: 
All aids except generative artificial intelligence are allowed for the weekly homework.

 

Three-hour final in-class problem set:
One personally created handwritten one-sided A4 page of notes.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam

30 minutes oral examination with no aids or preparation time. The oral examination will cover the entire material of the course, including the exercises from the exercise sessions.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.