A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds

par Pol van Hoften (King's College de Londres)

jeudi 21 nov. 2019, 14:00 → 15:00 Europe/Paris

Salle M7 (UMPA, ENS de Lyon)

It is an old idea of Serre that the classical Jacquet-Langlands correspondence between modular forms and quaternion modular forms can be realised geometrically. In this talk I will discuss an extension of these ideas to Siegel modular forms of genus two and paramodular level. We use this to prove the weight-monodromy conjecture for the Siegel threefold of paramodular level. Moreover we construct a geometric Jacquet-Langlands correspondence between GSp4 and a `definite' inner form, proving a conjecture of Ibukiyama.