NMAK16000U Algebraic Geometry 2 (AlgGeo2)

Volume 2021/2022

MSc Programme in Mathematics


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

Learning Outcome

Knowledge: To display knowledge and understanding of the course topics 
and content at a level suitable for further studies in Algebraic 

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

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

It is recommended that the students have taken the courses Algebraic Geometry (AlgGeo) and Homological Algebra (HomAlg).

Academic qualifications equivalent to a BSc degree is recommended.
4 hours lectures and 3 hours exercises per week for 9 weeks.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 143
  • Theory exercises
  • 27
  • Total
  • 206
Continuous feedback during the course of the semester
Feedback by final exam (In addition to the grade)

Continuous written individual feedback will be given on the hand-in assignments in order for students to improve their subsequent assignments, as well as on the final in-class test. Collective oral feedback will be given on students’ presentations in class.

7,5 ECTS
Type of assessment
Continuous assessment
Weekly homework (each weighted equally, accounting for 70% of the grade) and a final in-class problem set (accounting for 30% of the grade). You will have three hours for the in-class problem set.
Only certain aids allowed

All aids are allowed for the weekly homework. For the final in-class problem set, only written aids are allowed.

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

30 minutes oral exam with 30 minutes preparation time. During the preparation time all aids are allowed. During the examination no aids are allowed.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.