Number Theory Seminar

Speaker: Christian Johansson

Title: Eichler-Shimura theory for weight 1 modular forms

Abstract: For modular forms of weight at least 2, the singular/de Rham/étale (...) cohomology of modular curves beautifully synthesize their motivic nature and the Langlands correspondence. For weight 1 modular forms the Langlands correspondence is known, but there is no "motivic realization". I will describe a candidate for a "p-adic etale cohomology group" which should realize the Langlands correspondence for weight 1 modular forms, and give some indications and speculations about its motivic nature. This is a joint project, very much in its infancy, with James Newton, Jack Thorne, and Carl Wang-Erickson.