Schedule: 01.06.2020 - 31.08.2020
Contact information for the course (applies in this implementation):
Prof. Guillermo Mantilla-Soler: email@example.com, firstname.lastname@example.org
Details on the course content (applies in this implementation):
Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation):
This will be a pass-fail class, with mandatory assistance for those who want the pass grade. I will assign two or three homework sets and based on their completeness, and attendance, the fail or pass grade will be determined. There are no exams
Details on the course materials (applies in this implementation):
The following topics will be discussed:
- Introduction: How geometry determines arithmetic; classification of rational points of rational elliptic curves according to their genus, the trichotomy $g=0,1$ and $g \ge 2$.
- Projective geometry, quick review of algebraic curves, and properties of intersection in projective spaces. Singular points, rational parametrizations.
- Group structure on points of an elliptic curve.
- Weierstrass form of an elliptic curve. Isogenies.
- Complex and real elliptic curves. Uniformization theorem. The Weil Pairing over complex elliptic curves
- Mordell-Weil theorem. Rank, Mazur's theorem on torsion.
Course Homepage (valid 01.08.2018-31.07.2020):
Grading Scale (valid 01.08.2018-31.07.2020):
Additional information for the course (applies in this implementation):
Although I will not follow strictly any text book, the following three sources are good companions for the class:
- J. Silverman, J. Tate. Rational points on elliptic curves.
- J. Silverman. The arithmetic of elliptic curves}.
- N. Koblitz. Introduction to Elliptic curves and Modular forms.}
Details on the schedule (applies in this implementation):
The class will consist of a total of six lectures to take place via Zoom Mondays and Wednesdays from 12:15 to 14:00, starting on Monday 1.06 and finishing on Wednesday 18.06.