Elliptic curves/Elliptische Kurven

IMPORTANT NOTICE: On November 20, the lecture will take place between 16:00 and 18:00 in Room 119, Arnimallee 3. Both time and place are changed.

This is an introductory course on elliptic curves. Elliptic curves play important roles in mathematics as well as they have found applications in cryptography. Our emphasis will be on the arithmetic aspect of the theory (i.e. over finite fields and number fields). One of our goals is the proof of the Mordell-Weil theorem on the finite generatedness of the group of rational points of an elliptic curve over a number field. As for prerequisites, we assume basic algebra and (general) topology, but we do not assume a prior knowledge of algebraic geometry. Some knowledge of algebraic number theory may be helpful but not essential.

References

Milne's book Elliptic curves is our main reference. See also Silverman's book The arithmetic of elliptic curves and Fulton's Algebraic curves. Milne and Fulton's books are available on their websites.

Lectures and tutorials

Date and time: Lecture on Wednesday 14:00--16:00, Tutorial on Wednesday 12:00--14:00

Place: Lecture in A6/SR 031, Tutorial A3/SR 119

Tutorial: My intention is to have the participants ask questions and solve exercises on the board.

Language of instruction: English

What we did in class

What we did

Exercises

Exercises