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Abelian varieties and Galois module structure in global function fields. (English) Zbl 0863.11078
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.

11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
14K15 Arithmetic ground fields for abelian varieties
11G10 Abelian varieties of dimension \(> 1\)
Full Text: DOI EuDML
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