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

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## 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 |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 06 Apr 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/773 |

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