Text only print
Full screen print
Number Theory Seminar
Seminar information archive ～06/09｜Next seminar｜Future seminars 06/10～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
Future seminars
2026/06/10
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Ana Caraiani (Imperial College London)
Towards an Eichler-Shimura decomposition for ordinary p-adic Siegel modular forms
Ana Caraiani (Imperial College London)
Towards an Eichler-Shimura decomposition for ordinary p-adic Siegel modular forms
[ Abstract ]
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 in progress with James Newton and Juan Esteban Rodríguez Camargo that aims to compare them.
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 in progress with James Newton and Juan Esteban Rodríguez Camargo that aims to compare them.
2026/07/01
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
ISHIKURA Rintaro (University of Tokyo)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
ISHIKURA Rintaro (University of Tokyo)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
[ Abstract ]
We study p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity, whose A-parameters are tempered. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
We study p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity, whose A-parameters are tempered. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
