The Eisenstein family (Q2845443)

From the text: ``\textit{B. Mazur} and the author [The eigencurve. Lond. Math. Soc. Lect. Note Ser. 254, 1--113 (1998; Zbl 0932.11030)] defined a rigid analytic object called the eigencurve. This object parametrizes finite slope overconvergent normalized \(p\)-adic eigenforms. The Eisenstein family is a family of overconvergent modular forms whose existence was essential for the construction.''NEWLINENEWLINE ``The geometry of the eigencurve is still poorly understood.''NEWLINENEWLINE ``Based on the work of \textit{K. Buzzard} and \textit{L. J. P. Kilford} [Compos. Math. 141, No. 3, 605--619 (2005; Zbl 1187.11020)], and \textit{D. Roe} [Int. J. Number Theory 10, No. 7, 1791--1806 (2014; Zbl 1311.11030)], we state a general conjecture about the family of overconvergent Eisenstein series.''