Abstract
We show that if the restriction to the decomposition group at p of the p-adic Galois representation attached to one member of a Hida family of elliptic modular cusp forms is non-split then it is non-split for all but finitely many members of this family. We explain the relevance of this result to a question of Greenberg on the local splitting behavior of ordinary modular Galois representations.
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Ghate, E. (2004). On the Local Behavior of Ordinary Modular Galois Representations. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_8
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DOI: https://doi.org/10.1007/978-3-0348-7919-4_8
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