Rationalized Syntomic Cohomology

A few years ago, Bhatt-Morrow-Scholze introduced an invariant of p-adic formal schemes called syntomic cohomology, which has a close relationship to (étale-localized) algebraic K-theory. In a recent paper, Antieau-Mathew-Morrow-Nikolaus showed that, after inverting p, syntomic cohomology admits a concrete description in terms of more familiar invariants, such as de Rham and crystalline cohomology. In this talk, I'll explain an alternative perspective on their result, which avoids the use of K-theoretic methods.