Arithmetic of division fields
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- by Armand Brumer and Kenneth Kramer PDF
- Proc. Amer. Math. Soc. 140 (2012), 2981-2995 Request permission
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.References
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Additional Information
- Armand Brumer
- Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458
- MR Author ID: 272178
- 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
- MR Author ID: 194747
- Email: kkramer@gc.cuny.edu
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2981-2995
- MSC (2010): Primary 11F80; Secondary 11S15, 11G10, 11Y40
- DOI: https://doi.org/10.1090/S0002-9939-2012-11500-X
- MathSciNet review: 2917071