NMAK14034U Heights and Diophantine problems

Volume 2014/2015
Content

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.

Learning Outcome

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.

Algebra 3 or similar is an advantage
6 hours of lectures and 2 hours of tutorials each week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 2
  • Exercises
  • 14
  • Lectures
  • 42
  • Preparation
  • 148
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written examination, 2 hours under invigilation
Continuous assessment
Two written assignments count each 10%. A final written exam counts the remaining 80% of the grade
Aid
All aids allowed
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.
Criteria for exam assesment

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