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Corrigendum: Abelian n-division fields of elliptic curves and Brauer groups of product Kummer & abelian surfaces

Published online by Cambridge University Press:  30 November 2020

Anthony Várilly-Alvarado Open the ORCID record for Anthony Várilly-Alvarado [Opens in a new window]  and
Bianca Viray
Anthony Várilly-Alvarado
Affiliation:
Department of Mathematics MS 136, Rice University, Houston, TX77005, USA; E-mail: varilly@rice.edu
Bianca Viray
Affiliation:
University of Washington, Department of Mathematics, Box 354350, Seattle, WA98195, USA; E-mail: bviray@uw.edu

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There is an error in the statement and proof of [VAV17, Proposition 5.1] that affects the statements of [VAV17, Corollaries 5.2 and 5.3]. In this note, we correct the statement of [VAV17, Proposition 5.1] and explain how to rectify subsequent statements. In brief, for a statement about abelian Galois representations of a fixed level, ‘abelian’ should be replaced with ‘liftable abelian’ (Definition 1). Statements about abelian Galois representations of arbitrarily high level, however, remain unchanged because such representations give rise to liftable abelian Galois representations of smaller, but still arbitrarily high, level. Hence the main theorems of the paper remain unchanged.

Type
Number Theory
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e60
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

References

Várilly-Alvarado, Anthony and Viray, Bianca, Abeliann-division fields of elliptic curves and Brauer groups of product Kummer & abelian surfaces , Forum Math. Sigma 5 (2017), e26, 42, DOI 10.1017/fms.2017.16. MR3731278CrossRefGoogle Scholar