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過去の記録 ～10/04｜次回の予定｜今後の予定 10/05～
| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2026年10月13日(火)
17:00-18:00 数理科学研究科棟(駒場) 117号室
Dustin Clausen 氏 (IHES)
A refinement of Serre's conjecture
Dustin Clausen 氏 (IHES)
A refinement of Serre's conjecture
[ 講演概要 ]
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.
