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
DOI:
https://doi.org/10.1090/S0002-9939-2012-11500-X
Published electronically:
January 12, 2012
MathSciNet review:
2917071
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study the arithmetic of division fields of semistable abelian varieties The Galois group of
is analyzed when the conductor of
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:
https://doi.org/10.1090/S0002-9939-2012-11500-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.