Top-level heading

Towards a Jacquet-Langlands correspondence for function field modular forms

Categoria
Altro (categoria non censita)
Categoria non censita
Number Theory Seminar
Data e ora inizio evento
Data e ora fine evento
Aula
Altro (Aula esterna al Dipartimento)
Sede

INdAM, Dipartimento di Matematica, Sapienza Università di Roma

Aula esterna
Aula INdAM
Speaker
Paola Chilla
The Jacquet-Langlands correspondence relates modular forms for GL2 and for its inner forms, i.e. for unit groups of quaternion algebras, and was historically the first known example of Langlands transfer. It is natural to ask whether a similar correspondence holds in the realm of function fields. While the original analytic proof does not adapt to this setting, a geometric approach, based on étale cohomology computations, proves more fruitful. In this talk, I will discuss a first step towards a Jacquet-Langlands correspondence for function field modular forms. For a definite quaternion algebra ramified at exactly one finite place, I will associate Hecke eigensystems of rank 2 Drinfeld cusp forms to those arising from functions on quaternionic adèlic double quotients. The resulting Drinfeld cusp forms are new at the ramified prime, in the sense of Bandini and Valentino. The talk is based on the speaker’s PhD thesis, written under the supervision of Prof. Gebhard Böckle.
Contatti/Organizzatori
cherubini@altamatematica.it