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Local indecomposability of Tate modules of non-CM abelian varieties with real multiplication


Author: Haruzo Hida
Journal: J. Amer. Math. Soc. 26 (2013), 853-877
MSC (2010): Primary 14G35, 11G15, 11G18, 11F80; Secondary 11G10, 14L05
Published electronically: March 18, 2013
MathSciNet review: 3037789
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Abstract: Indecomposability of $ p$-adic Tate modules over the $ p$-inertia group for non-CM (partially $ p$-ordinary) abelian varieties with real multiplication is proven under unramifiedness of $ p$ in the base field and in the multiplication field.


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Additional Information

Haruzo Hida
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555
Email: hida@math.ucla.edu

DOI: https://doi.org/10.1090/S0894-0347-2013-00762-6
Keywords: Abelian variety, Tate module, real/complex multiplication, Galois representation, deformation
Received by editor(s): April 1, 2012
Received by editor(s) in revised form: December 27, 2012
Published electronically: March 18, 2013
Additional Notes: The author is partially supported by NSF grants DMS 0753991 and DMS 0854949
Article copyright: © Copyright 2013 American Mathematical Society