The $p$-completed cyclotomic trace in degree $2$

Johannes Anschütz, Arthur-César Le Bras

We prove that for a quasi-regular semiperfectoid ${\mathbb{Z}}_p^{\mathrm{cycl}}$-algebra $R$ (in the sense of Bhatt-Morrow-Scholze), the cyclotomic trace map from the $p$-completed $K$-t…