Jing Long Hoelscher : Bernoulli numbers and class numbers of cyclotomic function fields

Posted by , part of the Number Theory Seminar.

At

Oct. 27, 2010, 2 p.m.

In

SEO 427

Abstract

This talk will concern the divisibility of class numbers of cyclotomic function fields and their relation with Bernoulli numbers for rational function fields over finite fields. In number fields, the Herbrand-Ribet theorem gives a precise relation between the divisibility of class numbers of cyclotomic number fields and Bernoulli numbers. In function fields, the Herbrand's direction has been proven to be true, but the other direction has obvious counter-examples. Gekeler reformulated a conjecture similar to Ribet's theorem. This talk will report some recent progress towards the Gekeler's conjecture.