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Simplicity of twists of abelian varieties

Alex Bartel — 2015

Acta Arithmetica

We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.

Brauer relations in finite groups

Alex Bartel; Tim Dokchitser — 2015

Journal of the European Mathematical Society

If $G$ is a non-cyclic finite group, non-isomorphic $G$ -sets $X, Y$ may give rise to isomorphic permutation representations $ℂ [X] ≅ ℂ [Y]$ . Equivalently, the map from the Burnside ring to the rational representation ring of $G$ has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave–Bouc classification in the case of $p$ -groups.

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