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Archiv der Mathematik

, Volume 112, Issue 6, pp 615–622 | Cite as

Abelian varieties with finite abelian group action

  • Angel CaroccaEmail author
  • Herbert Lange
  • Rubí E. Rodríguez
Article
  • 16 Downloads

Abstract

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.

Keywords

Abelian variety Automorphism Finite groups 

Mathematics Subject Classification

14H40 14K10 

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Notes

Acknowledgements

We would like to thank Gabriele Nebe for pointing out a mistake in the first version of the paper.

Reference

  1. 1.
    Birkenhake, Ch., Lange, H.: Complex Abelian Varieties. Grundlehren der Mathematischen Wissenschaften, vol. 302, 2nd edn. Springer, New York (2004)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Matemática y EstadísticaUniversidad de la FronteraTemucoChile
  2. 2.Department MathematikUniversität ErlangenErlangenGermany

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