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2007.71: Invariants de classes: examples de non-annulation en dimension supérieure

2007.71: Jean Gillibert (2007) Invariants de classes: examples de non-annulation en dimension supérieure. Mathematische Annalen. ISSN 1432-1807

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DOI: 10.1007/s00208-007-0084-4

Abstract

The so-called class-invariant homomorphism ψ measures the Galois module structure of torsors—under a finite flat group scheme G—which lie in the image of a coboundary map associated to an isogeny between (Néron models of) abelian varieties with kernel G. When the varieties are elliptic curves with semi-stable reduction and the order of G is coprime to 6, it is known that the homomorphism ψ vanishes on torsion points. In this paper, using Weil restrictions of elliptic curves, we give the construction, for any prime number p > 2, of an abelian variety A of dimension p endowed with an isogeny (with kernel μ p ) whose coboundary map is surjective. In the case when A has rank zero and the p-part of the Picard group of the base is non-trivial, we obtain examples where ψ does not vanish on torsion points.

Item Type:Article
Subjects:MSC 2000 > 11 Number theory
MSC 2000 > 14 Algebraic geometry
MIMS number:2007.71
Deposited By:Miss Louise Stait
Deposited On:06 April 2007

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