Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Thursday, 12 June 2008

Gabriele Dalla Torre: Inequalities about the l-rank of the ideal class group

Abstract:

In this talk we study the action of a cyclic group G of order an odd prime l on an abelian group A and obtain some inequalities about the l-rank of A. Then we consider an algebraic extension K/Q and apply these results with G the Galois group of K/Q and A the ideal class group of K. As a special case we give a sufficient and necessary condition for the length of the Hilbert 3-class field tower of a cyclic absolute cubic extension to be greater than 1.