It is known that a p-adic family of modular forms does not necessarily specialize into a classical modular form at weight 1, unlike the modular forms of weight 2 or higher. We will explain how this obstruction to classicality leads to a ‘derived’ action on modular forms of weight 1, which can be understood as the so-called derived Hecke operator at p. We will also investigate the role of the derived action in the study of p-adic periods of the adjoint of the weight 1 modular forms.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
