Topological cyclic homology

Summary

Topological cyclic homology, written $TC$, is a spectrum built from topological Hochschild homology using its circle action and its Frobenius maps. It was introduced by Bökstedt, Hsiang and Madsen. It receives the cyclotomic trace from algebraic K-theory, and for nilpotent extensions of rings the two theories change in the same way. This makes $TC$ the main tool for computing K-theory of $p$-adic and local rings.