Speaker: Alexander Ivanov，波鸿鲁尔大学

Inviter: 聂思安

Title: Comparison of schematic and analytic local Langlands categories

Language: English

Time & Venue: 2026.09.24 10:30-11:30 南楼N820

Abstract: Recently Fargues–Scholze and Zhu independenly proposed two approaches to the geometrization of the Langlands correspondence over local non-Archimedean fields. The corresponding versions of the local Langlands categories are defined in terms of the stack of G-bundles on the Fargues–Fontaine curve within the framework of p-adic analytic geometry, respectively in terms of the stack of G-isocrystals over perfect schemes. The categorical local Langlands conjectures suggest that these two categories should be naturally equivalent. We will explain how to construct an equivalence between these categories with torsion coefficients. This is joint work with Gleason, Hamann, Lourenço and Zou.