The p-completed cyclotomic trace in degree 2

Arthur-César Le Bras (1) , Johannes Anschütz

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We prove that for a quasi-regular semiperfectoid Z cycl p-algebra R (in the sense of Bhatt-Morrow-Scholze), the cyclotomic trace map from the p-completed K-theory spectrum K(R; Zp) of R to the topological cyclic homology TC(R; Zp) of R identifies on π 2 with a q-deformation of the logarithm.

Domaines: Mathématiques [math]

Arthur-César Le Bras, Johannes Anschütz. The p-completed cyclotomic trace in degree 2. Annals of K-Theory, 2020. ⟨hal-03018441⟩