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ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS
Abstract Let p be a rational prime. Let F be a totally real number field such that F is unramified over p and the residue degree of any prime ideal of F dividing p is $\leq 2$ . In this paper, we show that the eigenvariety for $\mathrm {Res}_{F/\mathbb {Q}}(\mathit …