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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Arithmetic of division fields


Authors: Armand Brumer and Kenneth Kramer
Journal: Proc. Amer. Math. Soc. 140 (2012), 2981-2995
MSC (2010): Primary 11F80; Secondary 11S15, 11G10, 11Y40
Published electronically: January 12, 2012
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Abstract: We study the arithmetic of division fields of semistable abelian varieties $ A_{/\mathbb{Q}}.$ The Galois group of $ \mathbb{Q}(A[2])/\mathbb{Q}$ is analyzed when the conductor of $ A$ is odd and squarefree. The irreducible semistable mod 2 representations of small conductor are determined under GRH. These results are used in our paper Paramodular abelian varieties of odd conductor.


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Additional Information

Armand Brumer
Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458
Email: brumer@fordham.edu

Kenneth Kramer
Affiliation: Department of Mathematics, Queens College and the Graduate Center (CUNY), 65-30 Kissena Boulevard, Flushing, New York 11367
Email: kkramer@gc.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11500-X
PII: S 0002-9939(2012)11500-X
Keywords: Semistable Galois representation, transvection, stem field discriminant, bounded ramification.
Received by editor(s): March 26, 2011
Published electronically: January 12, 2012
Additional Notes: The research of the second author was partially supported by NSF grant DMS 0739346
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.