How many rational points can a curve over a finite field have?

Alp Bassa
Nanyang Technological University

Interesting from a purely number theoretic perspective and motivated additionally by various applications in coding theory and cryptography, this problem has been studied extensively. In this talk we will first give an introduction to several classical notions about algebraic curves, that will be used by this and several succeeding talks. We will then concentrate on rational points on curves over finite fields, especially the case of curves of large genus, introduce towers and sketch a Drinfeld modular interpretation for a new family of towers of function fields. These towers give examples with large limits over all non-prime finite fields.
More details about this and other explicit towers will be given on Wednesday by Arnaldo Garcia.
All new results in this talk are joint work with Beelen, Garcia and Stichtenoth.

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