Abelian varieties with finite abelian group action
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An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.
KeywordsAbelian variety Automorphism Finite groups
Mathematics Subject Classification14H40 14K10
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We would like to thank Gabriele Nebe for pointing out a mistake in the first version of the paper.