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Number Theory Seminar
Seminar information archive ～10/05｜Next seminar｜Future seminars 10/06～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2026/10/13
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Dustin Clausen (IHES)
A refinement of Serre's conjecture
Dustin Clausen (IHES)
A refinement of Serre's conjecture
[ Abstract ]
Gaitsgory-Raskin proved a remarkable theorem: in the function field setting, a certain natural vector space of (everywhere unramified) automorphic forms for GL_n is isomorphic to the global sections of the dualizing sheaf on a natural stack of Langlands parameters. I will describe an attempt to translate the statement of this theorem to the number field context, in the setting of mod p automorphic forms. The resulting conjectural statement is a variant of conjectures of Emerton-Zhu; for GL_2 it is a refinement of Khare-Wintenberger's theorem (formerly, Serre's conjecture) relating modular forms and Galois representations mod p.
Gaitsgory-Raskin proved a remarkable theorem: in the function field setting, a certain natural vector space of (everywhere unramified) automorphic forms for GL_n is isomorphic to the global sections of the dualizing sheaf on a natural stack of Langlands parameters. I will describe an attempt to translate the statement of this theorem to the number field context, in the setting of mod p automorphic forms. The resulting conjectural statement is a variant of conjectures of Emerton-Zhu; for GL_2 it is a refinement of Khare-Wintenberger's theorem (formerly, Serre's conjecture) relating modular forms and Galois representations mod p.
