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Number Theory Seminar
Seminar information archive ～03/03｜Next seminar｜Future seminars 03/04～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2026/03/11
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Kam Fai Tam (Xiamen Malaysia University)
A conjectural construction of Arthur Packets in Fargues-Scholze's categorical local Langlands correspondence
Kam Fai Tam (Xiamen Malaysia University)
A conjectural construction of Arthur Packets in Fargues-Scholze's categorical local Langlands correspondence
[ Abstract ]
The presentation consists of two parts. In the first part, we review -- from a novice point of view -- the categorical local Langlands correspondence due to Fargues and Scholze. Topics include: the structure of Bun_G and LocSys_{\hat G}, spectral action via Hecke operators, geometric Satake transform, and some conjectural consequences proposed by Fargues. (Apologies: the p-adic geometry underlying the relative Fargues-Fontaine curve is not included.)
In the second part, I will present a conjectural construction of Arthur packets in Fargues-Scholze's framework. This construction is based on the vanishing cycle functor introduced by Cunningham-Fiori-Moussaoui-Mracek-Xu, which is in turn inspired by Adams-Barbasch-Vogan for real groups. (A confession for curious audiences: this presentation offers essentially no new results. My goal is to illustrate how the legacy of James Arthur may influence other theories.)
The presentation consists of two parts. In the first part, we review -- from a novice point of view -- the categorical local Langlands correspondence due to Fargues and Scholze. Topics include: the structure of Bun_G and LocSys_{\hat G}, spectral action via Hecke operators, geometric Satake transform, and some conjectural consequences proposed by Fargues. (Apologies: the p-adic geometry underlying the relative Fargues-Fontaine curve is not included.)
In the second part, I will present a conjectural construction of Arthur packets in Fargues-Scholze's framework. This construction is based on the vanishing cycle functor introduced by Cunningham-Fiori-Moussaoui-Mracek-Xu, which is in turn inspired by Adams-Barbasch-Vogan for real groups. (A confession for curious audiences: this presentation offers essentially no new results. My goal is to illustrate how the legacy of James Arthur may influence other theories.)
