Wind from Rio, II

代数幾何講演会

“On tame towers and Artin-Schreier towers over finite fields”

Arnaldo Leite Pinto Garcia (IMPA, Brazil)

講演要旨: Since the fundamental work of A.Weil bounding the number of rational points on nonsingular projective curves over finite fields, which is equivalent to the validity of the Riemann Hypothesis for the associated Zeta-function, this subject has attracted the attention of many mathematicians. The interest grew further after the applications to Coding Theory iniciated by Goppa. The subject of this talk is the asymptotic behaviour of the number of rational points divided by the genus, as the genus tends to infinity. We give sufficient conditions for a good asymptotic behaviour in case of tame towers of curves and we give necessary conditions for a good asymptotic behaviour in case of towers of Artin-Schreier type. This is joint work with H.Stichtenoth.