5
$\begingroup$

Descent properties can be extremely useful for studying $\operatorname{TC}$ (topological cyclic homology), since it is a sheaf in many well behaved topologies.

I was wondering what is known about $\operatorname{TC}_\mathbb{Q}$ in this regard.

It seems clear to me that any site which has $\operatorname{TC}$ as a sheaf, and is also given in terms of a cd-structure will have $\operatorname{TC}_\mathbb{Q}$ as a sheaf, but I am particularly interested in the étale topology.

Improve this question
$\endgroup$
3
  • 2
    $\begingroup$ What do you call $TC$? $\endgroup$
    – Olivier Benoist
    Commented Mar 27, 2020 at 11:36
  • $\begingroup$ @OlivierBenoist topological cyclic homology $\endgroup$
    – Noah Riggenbach
    Commented Mar 27, 2020 at 13:59
  • 1
    $\begingroup$ Any localizing invariant valued in rational spectra satisfies étale descent, by an argument of Thomason; see the paper by Clausen, Mathew, Naumann, Noel. (Note that TC is not a localizing invariant in the strong sense which requires that it commutes with filtered colimits, but that is not necessary for Thomason's argument.) $\endgroup$
    – user147129
    Commented Mar 27, 2020 at 17:32

0

Reset to default

You must log in to answer this question.