NMAK14034U Heights and Diophantine problems
MSc Programme in Mathematics
The aim of this course is to discover the notion of height in
arithmetic (i.e. the height of an algebraic number) and in
arithmetic
geometry (i.e. the height of a point on a curve for example) and
the
spectacular results that it enables to prove. We will focus on the
arithmetic of projective curves, elliptic curves and abelian
varieties,
the Mordell conjecture and the Mordell-Weil theorem to be more
specific.
Knowledge: The student should be familiar with the main results
of the
topics of the course.
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: The student should be able to apply the theory to
solve
problems of moderate difficulty within the topics of the course.
In
particular calculate the height of a point on a curve, decide if
a
rational point on an abelian variety is a torsion point,
etc.
- Category
- Hours
- Exam
- 2
- Exercises
- 14
- Lectures
- 42
- Preparation
- 148
- Total
- 206
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Written examination, 2 hours under invigilationContinuous assessmentTwo written assignments count each 10%. A final written exam counts the remaining 80% of the grade
- Aid
- All aids allowed
NB: If the exam is held at the ITX, the ITX will provide you a computer. Private computer, tablet or mobile phone CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
Resubmission of failed assignments and a 30 minutes oral exam with several internal examiners. The assignments must be resubmitted no later than two weeks before the beginning of the re-exam week.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK14034U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Fabien Pazuki (7-6872637c776d6b426f63766a306d7730666d)