Abstract

A classical point of the Coleman–Mazur eigencurve is said to be exceptional if the map to weight space is nonétale at that point. This paper revisits the $p$-adic elliptic Stark conjecture of Darmon et al. (Forum Math. Pi 3 (2015), art. id. e8) concerning a triple $(f,g,h)$ of classical modular forms of weights $(2,1,1)$, and extends it to the setting where the $p$-stabilised eigenform $g$ corresponds to such an exceptional point.

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