English

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

K-Theory and Homology 2021-05-17 v2 Number Theory

Abstract

We prove that for a quasi-regular semiperfectoid Zpcycl\mathbb{Z}_p^{\rm cycl}-algebra RR (in the sense of Bhatt-Morrow-Scholze), the cyclotomic trace map from the pp-completed KK-theory spectrum K(R;Zp)K(R;\mathbb{Z}_p) of RR to the topological cyclic homology TC(R;Zp)\mathrm{TC}(R;\mathbb{Z}_p) of RR identifies on π2\pi_2 with a qq-deformation of the logarithm.

Keywords

Cite

@article{arxiv.1907.10530,
  title  = {The $p$-completed cyclotomic trace in degree $2$},
  author = {Johannes Anschütz and Arthur-César Le Bras},
  journal= {arXiv preprint arXiv:1907.10530},
  year   = {2021}
}
R2 v1 2026-06-23T10:29:35.926Z