## Number Theory Seminar

Tuesday 23 January 2007, MR13, 2:30pm

Geometric Galois module structure and abelian varieties of higher dimension
Jean Gillibert (Manchester)

Abstract:

The so-called class-invariant homomorphism $\psi_n$, introduced by M. J. Taylor, measures the Galois module structure of (rings of integers of) extensions of the form $K(\frac{1}{n}P)/K$, where $K$ is a number field, $P$ is a $K$-rational point on an abelian variety $A$, and $n>1$ is an integer. When $A$ is an elliptic curve and $n$ is coprime to 6, then $\psi_n$ vanishes on torsion points. We explain here how, using Weil restrictions of elliptic curves, it is possible to construct abelian varieties of higher dimension for which this vanishing result is no longer true.