Invariants de classes : exemples de non-annulation en dimension supérieure

GILLIBERT, Jean

doi:10.1007/s00208-007-0084-4

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GILLIBERT, Jean
Institut de Mathématiques de Bordeaux [IMB]

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Ce document a été publié dans

Mathematische Annalen. 2007, vol. 338, n° 2, p. 475-495

Springer Verlag

Résumé en anglais

The so-called class-invariant homomorphism $\psi$ 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, is is known that the homomorphism $\psi$ 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 $\mu_p$) 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 $\psi$ does not vanishes on torsion points.< Réduire

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