Towards an Eichler-Shimura Decomposition for Ordinary $p$-adic Siegel Modular Forms

Apr 25, 2024, 11:00 AM
1h
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

Speaker

Prof. Ana Caraiani (Imperial College London)

Description

There are two different ways to construct families of ordinary $p$-adic Siegel modular forms. One is by $p$-adically interpolating classes in Betti cohomology, first introduced by Hida and then given a more representation-theoretic interpretation by Emerton. The other is by $p$-adically interpolating classes in coherent cohomology, once again pioneered by Hida and generalised in recent years by Boxer and Pilloni. I will explain these two constructions and then discuss joint work with James Newton and Juan Esteban Rodríguez Camargo, very much in progress, that aims to compare them.

Presentation materials

There are no materials yet.