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Number Theory Seminar
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2026/05/27
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
ONISHI Haruto (University of Tokyo)
Geometric realization of the local Langlands and local Jacquet-Langlands correspondences for GL(4) in a partially ramified case
ONISHI Haruto (University of Tokyo)
Geometric realization of the local Langlands and local Jacquet-Langlands correspondences for GL(4) in a partially ramified case
[ Abstract ]
The local Langlands correspondence and the local Jacquet-Langlands correspondence are realized using Lubin-Tate spaces. However, only limited cases of the correspondence between supercuspidal representations and L-parameters have been geometrically realized by algebraic varieties defined by explicit equations. There are several works in which such algebraic varieties are obtained as reductions of special affinoids in the Lubin-Tate space at infinite level. Even in the essentially tame case, where the correspondence is explicitly described by Bushnell–Henniart, such affinoids had previously been constructed only in the unramified and totally ramified cases. In this talk, I will explain a result constructing such affinoids in a partially ramified case, under certain special assumptions.
The local Langlands correspondence and the local Jacquet-Langlands correspondence are realized using Lubin-Tate spaces. However, only limited cases of the correspondence between supercuspidal representations and L-parameters have been geometrically realized by algebraic varieties defined by explicit equations. There are several works in which such algebraic varieties are obtained as reductions of special affinoids in the Lubin-Tate space at infinite level. Even in the essentially tame case, where the correspondence is explicitly described by Bushnell–Henniart, such affinoids had previously been constructed only in the unramified and totally ramified cases. In this talk, I will explain a result constructing such affinoids in a partially ramified case, under certain special assumptions.
