Wenhan Dai

Seminar Beyond Fargues-Scholze

The purpose of this weekly seminar is to study some of the recent works that are built on Fargues-Scholze. We will focus on those works in the Langlands program. All talks will be given by participants, and each meeting will be about 110 minutes, with a ten minutes break in the middle.

• Organizer: Zhiyou Wu (MCM).
• Time: 13:00–15:00 Wednesdays (starting on March 1).
• Venue: Jingchun Yuan 78301.

Syllabus

• (3/1) Zhiyou Wu: Overview.
• (3/8) Xiangqian Yang: The condensed group homology computations [Zou, §3,4].
• (3/15) Xiangqian Yang: Finish of the proof [Zou, §5, 6].
• (3/29) Daming Zhou: Geometric class field theory [Far, §1-5].
• (4/5) Heng Du: Proof [Far, §7].
• (4/12) Yichao Tian: Averaging functors I [AB, §4, 5.1-5.4]. (notes)
• (4/19) Daxin Xu: Averaging functors II [AB, §5.5-5.6, 6].
• (4/26) Zeyu Wang: Fargues’ conjecture in the irreducible case [AB, §7]. (notes)
• (The meeting is canceled during the PKU spring holiday.)
• (5/17) Liang Xiao: Review of the Kottwitz conjecure and the classical approaches, [HKW, §1,2] and the reference in the introduction, notably the work of Strauch and Mieda.
• (5/24) Weizhe Zheng: The Lefschetz-Verdier trace formula [HKW, §4]. (notes)
• (5/31) Jiahao Niu: Local terms on the BdR-affine Grassmannian [HKW, §5.1-5.3]. (notes)
• (No meeting during the Hong Kong conference.)
• (6/14) Jilong Tong: Applications I [HKW, §6.1-6.3]. (notes)
• (6/21) Wen-wei Li: Transfer [HKW, §3]. (notes)
• (Canceled) Zhiyou Wu: Applications II [HKW, §6.4-6.6].

References

1. [AB] Johannes Anschütz and Arthur-César Le Bras Averaging functors in Fargues’ program for GL(n).
2. [Far] Laurent Fargues, Simple connexite des fibres d’une application d’Abel-Jacobi et corps de classe local.
3. [HKW] David Hansen, Tasho Kaletha, and Jared Weinstein, On the Kottwitz conjecture for local shtuka spaces.
4. [SW] P. Scholze and J. Weintein, Moduli of p-divisible groups.
5. [Zou] Konrad Zou, The categorical form of Fargues’ conjecture for tori.