Abelian varieties and Galois module structure in global function fields (Q1346330)

This paper gives a function field analogue of the work of M. J. Taylor on the Galois module structure of certain Kummer orders associated to points on abelian varieties over number fields. A condition in terms of the point is given which implies that the Galois module is not free. Moreover a geometric interpretation of the construction is given. This is used to show how the zeta-function of the abelian variety gives precise information on the question of which modules arise in this way.