# Crystalline comparison of Ainf-cohomology

## Location

Abstract: A major goal of p-adic Hodge theory is to relate arithmetic structures coming from various cohomology theories of p-adic varieties. Such comparisons are usually achieved by constructing intermediate cohomology theories. A somewhat recent successful theory, namely the Ainf-cohomology, has been invented by Bhatt--Morrow--Scholze, originally via perfectoid spaces. In this talk, I will describe a simpler approach to prove the comparison between Ainf-cohomology and the crystalline cohomology over Fontaine's period ring Acris, using the de Rham comparison and flat descent of cotangent complexes. Time permitting, we discuss some work in progress in the logarithmic case.