世話人: 沖 泰裕, トーマス・ガイサ, 水澤 靖

連絡先 (沖): oki [at] rikkyo.ac.jp

立教大学池袋キャンパスへのアクセス: https://www.rikkyo.ac.jp/access/ikebukuro/

次回の予定

【2025年度第3回】

• 日時: 2025年12月4日 (木), 17:15～18:15

• 会場: 池袋キャンパス5号館 5209号室

• 講演者: 伊藤 和広 氏 (東北大学)

• タイトル: Affine Grassmannians and close fields

• アブストラクト: Let $G$ be a split reductive group over the ring of integers and $\mu$ a cocharacter of $G$. For a non-archimedean local field $F$ of characteristic $p$ with finite residue field $k$, we have the Schubert variety over $k$ corresponding to $\mu$ in the affine Grassmannian of $G_F$. On the other hand, for a non-archimedean local field $E$ of characteristic zero with the same residue field $k$, we can consider the Witt vector Grassmannian of $G_E$ introduced by Zhu, and the Schubert variety corresponding to $\mu$ inside it, which is known to be (the perfection of) a projective variety over $k$.
  In this talk, we show that if the absolute ramification index of $E$ is sufficiently large, then the Schubert varieties corresponding to $\mu$ in these two settings are isomorphic to each other (after taking perfections). This result aligns with the Deligne-Kazhdan philosophy of close fields. In order to do this, we establish a certain representability result for a version of affine Grassmannian defined using a moduli space of non-archimedean local fields introduced by Li-Huerta.
 If time permits, I will also discuss potential applications to orbital integrals for $G_F$.

  This talk is based on joint work with Sebastian Bartling.

画像: 東京にて, 世話人 (沖) による撮影