Kaixing Cao: A Motivic Comparison of p-adic Cohomology Theories for Rigid Analytic Varieties

Number Theory Seminar: Kaixing Cao (University of Milano)

A Motivic Comparison of p-adic Cohomology Theories for Rigid Analytic Varieties

In this talk, we develop a motivic approach to comparison theorems in p-adic Hodge theory. Using these methods, we establish a comparison isomorphism between de Rham--Fargues--Fontaine cohomology and overconvergent Hyodo--Kato cohomology. This result confirms that de Rham--Fargues--Fontaine cohomology realizes the conjectural vector bundle–valued cohomology theory on the Fargues--Fontaine curve envisioned by Fargues and Scholze. Furthermore, we show that, within the motivic framework, this construction coincides with the décalage-based theory introduced by Le Bras and Bosco.