Algebraic K-theory can be studied by relating it to other invariants, such as topological cyclic homology, as well as through cohomology theories. In this talk, I will discuss an instance of their interactions, namely that how one can reconstruct Thomason’s filtration on T(1)-localized algebraic K-theory of the generic fiber of p-adic rings through topological cyclic homology, and how this recovers the étale-prismatic comparison theorem.
