Geometric Aspects of the $p$-adic Locally Analytic Langlands Correspondence

The talk presents cutting-edge research in arithmetic geometry, specifically the geometrization of the p-adic Langlands program. The speaker, Arthur-César Le Bras, is a recognized expert, and the work is joint with Anschütz, Rodriguez Camargo, and Scholze, indicating high credibility. The content is highly technical, aimed at specialists, and assumes familiarity with advanced concepts such as Fargues-Scholze stacks, prismatic cohomology, and locally analytic representations. The presentation is rigorous, with careful statements of what is known and what remains conjectural. The speaker clearly distinguishes between established results and conjectural expectations, which is a sign of scientific honesty. The construction of the stack Bun_G via near-perfect rings and its embedding of locally analytic representations is a significant contribution. The discussion of the Hecke action, while incomplete, provides valuable insights into the expected structure. The examples, particularly the Lubin-Tate case, illustrate the abstract framework concretely. The talk does not overclaim; instead, it openly acknowledges the limitations and open questions, which is appropriate for ongoing research. The sources cited are primarily the speaker’s own work and related literature, which is standard for a research talk. The title accurately reflects the content. Overall, this is an excellent, high-level research presentation that contributes to the advancement of the field.

The title accurately reflects the content: the talk focuses on geometric aspects of the p-adic locally analytic Langlands correspondence, specifically the geometrization program.

9/10

Talk by a leading expert (Université de Strasbourg) presenting recent joint work with Anschütz, Rodriguez Camargo, Scholze. The content is highly technical, based on established mathematical frameworks (Fargues-Scholze, prismatic cohomology). The presentation is rigorous, with clear caveats about conjectural aspects. No obvious errors or overclaims.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction and recap of previous talk: definition of Bun_G via near-perfect rings and Fargues-Fontaine curves.
• 05:00Discussion of the pullback description of Bun_G and the open immersion from the classifying stack of G(Q_p) into Bun_G.
• 10:00Fully faithful embedding of solid locally analytic representations into sheaves on Bun_G.
• 15:00Introduction of the spectral side: moduli stacks LS_{D1}^{GL_n} and its derived variant.
• 20:00Formulation of the conjectural locally analytic geometric Langlands equivalence.
• 25:00Discussion of the Hecke action as the fundamental structure connecting the two sides.
• 30:00First example of Hecke action: Lubin-Tate case for GL_2, minuscule cocharacter (1,0).
• 35:00Description of the Hecke stratum as the perfect analytic prismatization of P^1 modulo automorphisms.
• 40:00Discussion of open questions and limitations in defining the full Hecke stack.

• Carmin.tv — Video platform for mathematics, hosting this talk and related content.

• Fargues-Scholze's geometrization of the local Langlands correspondence — Provides the foundational framework for the geometric Langlands program in the p-adic setting.