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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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