Notes on the $$\mathbb A_{{\mathrm {inf}}}$$-Cohomology of Integral p-Adic Hodge Theory

We present a detailed overview of the construction of the \(\mathbb A_{{\mathrm {inf}}}\)-cohomology theory from the preprint Integral p-adic Hodge theory, joint with Bhatt and Scholze. We focus particularly on the p-adic analogue of the Cartier isomorphism via relative de Rham–Witt complexes.