In recent years, the study of the algebraic K-theory space K (R) of a ring R has been
approached by the introduction of spaces with a more homological flavor. One collection of …

Let f: A-~ B be a map of rings up to homotopy (or" FSP's", see eg [B61],[B53] or Definition 3.1
below). When is it possible to give a good description of the relative algebraic K-theory …

The present paper is an attempt to give an overview of topological cyclic homology and its
relation to algebraic K-theory. In the “classical'setting, al-gebraic K-theory associates to a …

Recall that a ring _ (without unit) is said to possess th f in algebraic K-theory if for every ring
extension sV>-i-9> Y the K*-groups of, 9 and Y are related to each other by the natural long …

Relative Algebraic K-Theory and Cyclic Homology Page 1 Annals of Mathematics, 124 (1986),
347-402 Relative algebraic K-theory and cyclic homology By THOMAS G. GOODWILLIE …

IT was shown in [3] that for a l-connected space X, R,+ 1 (X)@ Q, the reduced Waldhausen
algebraic K-theory of X, and He,(X; Q), the reduced cyclic homology of the Q-differential …

The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological
refinement of cyclic homology. The target is naturally mapped to topological Hochschild …

Algebraic K-Theory plays an important role in many areas of modern mathematics: most
notably algebraic topology, number theory, and algebraic geometry, but even including …

Let KR be a nonconnective spectrum whose homotopy groups give the algebraic K-theory of
the ring R. We give a description of the associated homology theory KR*(X) associated to …

1) When X can be expressed as a subscheme of projective space (ie is quasiprojective) the"
moving lemma" says there are cycles within the given classes whose intersection has …