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On the local behavior of ordinary modular Galois representations. (English) Zbl 1166.11330

Cremona, John (ed.) et al., Modular curves and Abelian varieties. Based on lectures of the conference, Bellaterra, Barcelona, July 15–18, 2002. Basel: Birkhäuser (ISBN 3-7643-6586-2/hbk). Prog. Math. 224, 105-124 (2004).
Summary: 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.
See also the joint article by the author and V. Vatsal [Ann. Inst. Fourier 54, No. 7, 2143–2162 (2004; Zbl 1131.11341)].
For the entire collection see [Zbl 1032.11002].

MSC:

11F80 Galois representations
11F33 Congruences for modular and \(p\)-adic modular forms
14L15 Group schemes

Citations:

Zbl 1131.11341
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