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1.1. Topological cyclic homology is the codomain of the cyclotomic trace from algebraic i^-theory trc: K (L)-> TC (L).

It was defined in [2] but for our purpose the exposition in [6] is more convenient. The cyclotomic trace is conjectured to induce a homotopy equivalence after p-completion for a certain class of rings including the rings of algebraic integers in local fields of possitive residue characteristic p. We refer to [11] for a detailed discussion of conjectures and results in this direction. Recently B. Dundas and R. McCarthy have proven that the stabilization of algebraic i^-theory is naturally equivalent to topological Hochschild homology,