Workshop on Geometrization of Local Langlands Correspondence
The goal of this workshop is to understand the recent progress by Fargues–Scholze on the geometrization of local Langlands correspondence. The main reference is the long manuscript [FS] by Fargues–Scholze. Hopefully, with enough time for discussion, we may find some applications of the results in the near future.
Organizer: Liang Xiao .Time: Jan 2–13, all talks will be at 1–2:30pm or 3–4:30pm on weekdays (except for the last day).Venue: Tencent Meeting (The room is closed now ).
Schedule
Yichao Tian: Introduction part I, §I. (notes )Yichao Tian: Introduction part II, §I. (notes )Jilong Tong: Fargues-Fontaine curve and vector bundles, §II.1–II.2. (notes: part 1 , part 2 )Heng Du: Fargues-Fontaine curve and vector bundles, §II.3. (notes )Miaofen Chen: $\mathrm{Bun}_G$, §III. (notes )Weizhe Zheng: ULA sheaves, §IV.1–IV.2. (notes )Shanwen Wang: More geometry of diamonds, §IV.3–IV.4. (notes )Yong-Suk Moon: Hyperbolic localization and Drinfeld’s lemma, §IV.5–IV.7. (notes )Jiahao Niu: $D_{\mathrm{et}}(\mathrm{Bun}_G)$, §V. (notes )Jingren Chi: $\mathbb{B}_{\mathrm{dR}}$-affine Grassmannian, §VI.1–VI.4. (notes )Xu Shen: Geometric Satake I, §VI.5–VI.8. (notes )Xu Shen: Geometric Satake II, §VI.9–VI.12. (notes )Yixiao Li: Solid sheaves, §VII.1–VII.3. (notes )Yixiao Li: $D_{\mathbf{\square}}(X)$, §VII.4–VII.7. (notes )Xiangqian Yang: Stack and coarse moduli of L-parameters, §VIII.1–VIII.3. (notes )Zeyu Wang: Excursion operators, §VIII.4–VIII.5. (notes )Yong-Suk Moon: Hecke actions I, §IX. (notes )Xiangqian Yang: Hecke actions II, §IX. (notes )Koji Shimizu: The spectral action, §X. (notes )Zhiyou Wu: Fargues–Scholze and other approaches to local Langlands. (notes )Jize Yu: Mixed characteristic Arkhipov-Bezrukavnikov equivalence. (notes )
Reference
[FS] Laurent Fargues and Peter Scholze, Geometrization of the local Langlands correspondence, preprint.