Seminar on Curves over Finite Fields

Andreas Hochenegger and I offered a seminar in the summer semester of 2009 on curves over finite fields and their applications. We covered a large portion of the material in section II of Stepanov's book.

Talks Given:

Topic Reference Date Speaker
Introduction to algebraic geometry [Step] 4.1 April 16 L. Kästner
Non-Singular curves [Step] 4.2 April 23 K. Kubjas
Divisors and the Riemann-Roch theorem [Step] 4.3 and 4.4 April 30 I. Sharankon
Rational points and divisors I [Step] 5.1 up to prop. 5.4 May 14 L. Hinsch
Rational points and divisors II [Step] 5.1 starting after prop. 5.4 May 28 N. Ilten
The zeta function of a curve I [Step] 5.2; definition and infinite product June 4 M. Merz
The zeta function of a curve II [Step] 5.2; functional equation and rational points June 11 J. Sanchez
Bounds on rational points [Step] 6.1 and 6.3 June 25 M. Wandel
Coding theory basics [Step] 1.3, 2.1, and 2.3 July 2 L. Petersen
Goppa codes [Step] 10.1 and 13.1 July 9 N. Ilten
Elliptic curve cryptography [Silv] July 16 F. Garbe

References