Speaker: Prof. Heng Du，Tsinghua University

Title: From p-adic Hodge theory to relative shtukas—and back

Language: Chinese

Time & Venue: 2026.05.22 16:45-17:45 MCM110

Abstract: The category of p-adic local shtukas was introduced by Scholze as a mixed-characteristic analog of Drinfeld’s shtukas. Its formulation was made possible by several major developments in p-adic Hodge theory, including Scholze’s theory of perfectoid spaces and diamonds, the foundational work of Fargues and Fontaine on the Fargues–Fontaine curve, and the framework of relative p-adic Hodge theory developed by Kedlaya and Liu. Since their introduction, p-adic local shtukas have played a central role in recent progress toward the geometrization of the local Langlands program. In this talk, I will explain how ideas from this circle of developments can also be brought back to p-adic Hodge theory. In particular, I will show that reasonable categories of arithmetic Z_p-local systems can be embedded, in a compatible way, into the category of relative shtukas. As an application, I will discuss how this viewpoint leads to new insights into the relative p-adic monodromy conjecture.