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A local analysis of congruences in the $$(p,p)$$ case. I. (English) Zbl 1072.11506
Summary: Given an irreducible, modular, mod $$p$$ representation $$p$$, we analyse the local components at $$p$$ of newforms $$f$$ which give rise to it.

##### MSC:
 11F33 Congruences for modular and $$p$$-adic modular forms 11F32 Modular correspondences, etc. 11F80 Galois representations 11F85 $$p$$-adic theory, local fields
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