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Abelian varieties with finite abelian group action

Authors
  • Carocca, Angel1
  • Lange, Herbert2
  • Rodríguez, Rubí E.1
  • 1 Universidad de la Frontera, Departamento de Matemática y Estadística, Casilla 54-D, Temuco, Chile , Temuco (Chile)
  • 2 Universität Erlangen, Department Mathematik, Erlangen, Germany , Erlangen (Germany)
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Springer International Publishing
Publication Date
Apr 20, 2019
Volume
112
Issue
6
Pages
615–622
Identifiers
DOI: 10.1007/s00013-018-1291-9
Source
Springer Nature
Keywords
License
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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.

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