References
[A]Adams, J. F., A periodicity theorem in homological algebra.Proc. Cambridge Philos. Soc., 62 (1966), 365–377.
[BF]Bousfield, A. K. &Friedlander, E. M., Homotopy theory of Γ-spaces, spectra and bisimplicial sets, inGeometric Applications of Homotopy Theory, Vol. II (Evanston, IL, 1977), pp. 80–130. Lecture Notes in Math., 658. Springer-Verlag, Berlin-New York, 1978.
[BK]Bousfield, A. K. &Kan, D. M.,Homotopy Limits, Completions and Localizations. Lecture Notes in Math., 304. Springer-Verlag, Berlin-New York, 1972.
[Bö1]Bökstedt, M., Topological Hochschild homology. To appear inTopology.
[Bö2]Bökstedt, M., Carlsson, G., Cohen, R., Goodwillie, T. G., Hsiang, W. C. &Madsen, I., The algebraic K-theory of simply connected spaces.Duke Math. J., 84 (1996), 541–563.
[Bö3]Bökstedt, M., Hsiang, W. C. &Madsen, I., The cyclotomic trace and algebraic K-theory of spaces.Invent. Math., 111 (1993), 463–539
[Bö4]Bökstedt, M. &Madsen, I., Topological cyclic homology of the integers.Astérisque, 226 (1994), 57–143.
[Bö5]—, Algebraic K-theory of local number fields: the unramified case, inProspects in Topology (Princeton, NJ, 1994), pp. 28–57. Ann. of Math. Stud., 138. Princeton Univ. Press, Princeton, NJ, 1995.
[DGM]Dundas, B. I., Goodwillie, T. G. & McCarthy, R., In preparation.
[DM]Dundas, B. I. &McCarthy, R., Stable K-theory and topological Hochschild homology.Ann. of Math., 140 (1994), 685–701.
[Dw]Dwyer, W. G., Twisted homological stability for general linear groups.Ann. of Math., 111 (1980), 239–251.
[EKMM]Elmendorf, A. D., Kriz, I., Mandell, M. A. &May, J. P.,Rings, Modules, and Algebras in Stable Homotopy Theory. With an Appendix by M. Cole. Math. Surveys Monographs, 47. Amer. Math. Soc., Providence, RI, 1997.
[FJ]Farrell, F. T. &Jones, L. E., Rigidity in geometry and topology, inProceedings of the International Congress of Mathematicians (Kyoto, 1990), pp. 653–663. Math. Soc. Japan, Tokyo, 1991.
[G1]Goodwillie, T. G., Relative algebraic K-theory and cyclic homology.Ann. of Math., 124 (1986), 347–402.
[G2]Goodwillie, T. G., Letter to F. Waldhausen, July 13, 1988.
[G3]—, Calculus II: Analytic functors.K-Theory, 5 (1992), 295–332.
[G4]Goodwillie, T. G., Notes on the cyclotomic trace (March 23, 1990). Lecture notes from a lecture series given at MSRI during the spring of 1990.
[G5]—, The differential calculus of homotopy functors, inProceedings of the International Congress of Mathematicians (Kyoto, 1990), pp. 621–630. Math. Soc. Japan, Tokyo, 1991.
[HM]Hesselholt, L. &Madsen, I., On the K-theory of finite algebras over Witt vectors of perfect fields.Topology, 36 (1997), 29–101.
[I]Igusa, K., The stability theorem for smooth pseudoisotopies.K-Theory, 2 (1988), 1–355.
[KR]Klein, J. R. &Rognes, J., The fiber of the linearization mapA(*)→K(Z).Topology, 36 (1997), 829–848.
[L]Lydakis, M., Smash products and Γ-spaces. To appear inJ. Pure Appl. Algebra.
[M1]Madsen, I., Algebraic K-theory and traces, inCurrent Developments in Mathematics (R. Bott, A. Jaffe and S. T. Yau, eds.), pp. 191–323. International Press, 1995.
[M2]—, The cyclotomic. trace in algebraic K-theory, inFirst European Congress of Mathematics, Vol. II (Paris, 1992), pp. 213–241. Progress in Math., 120. Birkhäuser, Basel, 1994.
[Mc]McCarthy, R., Relative algebraic K-theory and topological cyclic homology.Acta Math., 179 (1997), 197–222.
[PW]Pirashvili, T. &Waldhausen, F., Mac Lane homology and topological Hochschild homology.J. Pure Appl. Algebra, 82 (1992), 81–98.
[Q1]Quillen, D. G., Finite generation of the groupsK i of rings of algebraic integers, inAlgebraic K-Theory I—Higher K-Theories (Battelle Institute, 1972), pp. 179–198. Lecture Notes in Math., 341. Springer-Verlag, Berlin-New York, 1973.
[Q2]—,Homotopical Algebra. Lecture Notes in Math., 43. Springer-Verlag, Berlin-New York, 1967.
[R]Rognes, J., Algebraic K-theory of the two-adic integers. To appear inJ. Pure Appl. Algebra.
[Sä]Schwänzl, R., Staffeldt, R. &Waldhausen, F., Stable K-theory and topological Hochschild homology ofA ∞ rings.Contemp. Math., 199 (1996), 161–173.
[Se]Schwede, S., Stable homotopy of algebraic theories. Thesis, Bielefeld, 1996.
[W1]Waldhausen, F., Algebraic K-theory of spaces, concordance, and stable homotopy theory, inAlgebraic Topology and Algebraic K-Theory (Princeton, NJ, 1983), pp. 392–417. Ann. of Math. Stud., 113. Princeton Univ. Press, Princeton, NJ, 1987.
[W2]—, Algebraic K-theory of generalized free products.Ann. of Math., 108 (1978), 135–256.
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The author was supported by the Danish Research Academy
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Dundas, B.I. Relative K-theory and topological cyclic homology. Acta Math. 179, 223–242 (1997). https://doi.org/10.1007/BF02392744
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DOI: https://doi.org/10.1007/BF02392744