This text covers the connection between algebraic K-theory and Bokstedt, Hsiang and Madsen's topological cyclic homology and proves the difference between the theories are locally constant. It contains a proof of the integral Goodwillie ICM 1990 conjecture.

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and...