Cyclotomic trace

Summary

The cyclotomic trace is a natural map $K(R) \to TC(R)$ from the algebraic K-theory spectrum of a ring to its topological cyclic homology. It was constructed by Bökstedt, Hsiang and Madsen. It refines the Dennis trace map and its topological version $K(R) \to THH(R)$. For nilpotent extensions it detects relative K-theory exactly, which makes it the main tool for computing K-groups of local and $p$-adic rings.