Topological cyclic homology of the integers

Bökstedt, M. ; Madsen, I.

K

-theory - Strasbourg, 1992, Astérisque, no. 226 (1994), pp. 57-143

MR Zbl | 1 citation dans Numdam

@incollection{AST_1994__226__57_0,
     author = {B\"okstedt, M. and Madsen, I.},
     title = {Topological cyclic homology of the integers},
     booktitle = {$K$-theory - Strasbourg, 1992},
     series = {Ast\'erisque},
     pages = {57--143},
     year = {1994},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {226},
     mrnumber = {1317117},
     zbl = {0816.19001},
     language = {en},
     url = {https://www.numdam.org/item/AST_1994__226__57_0/}
}

TY  - CHAP
AU  - Bökstedt, M.
AU  - Madsen, I.
TI  - Topological cyclic homology of the integers
BT  - $K$-theory - Strasbourg, 1992
AU  - Collectif
T3  - Astérisque
PY  - 1994
SP  - 57
EP  - 143
IS  - 226
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1994__226__57_0/
LA  - en
ID  - AST_1994__226__57_0
ER  -

%0 Book Section
%A Bökstedt, M.
%A Madsen, I.
%T Topological cyclic homology of the integers
%B $K$-theory - Strasbourg, 1992
%A Collectif
%S Astérisque
%D 1994
%P 57-143
%N 226
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1994__226__57_0/
%G en
%F AST_1994__226__57_0

Bökstedt, M.; Madsen, I. Topological cyclic homology of the integers, dans $K$-theory - Strasbourg, 1992, Astérisque, no. 226 (1994), pp. 57-143. https://www.numdam.org/item/AST_1994__226__57_0/

Bibliographie
Cité par

1. J. F. Adams, Infinite loop spaces, Ann. Math. Studies No. 90 Princeton University Press (1978) | MR | Zbl

2. J. F. Adams, Prerequisites (on equivariant theory) for Carlsson's lecture, LNM vol. 1051 (1984), Springer-Verlag | MR | Zbl

3. J. M. Boardman, Conditionally convergent spectral sequences, preprint, John Hop kins University (1981)

4. A. K. Bousfield, The localization of spectra with respect to homology, Topology 18 (1979), 257-281 | MR | Zbl | DOI

5. A. K. Bousfield, D. M. Kan, Homotopy Limits, Completions and Localizations, LNM 304 (1987), Springer Verlag. | Zbl | MR

6. G. E. Bredon, Equivariant cohomology theories, LNM, vol 34 (1967), Springer-Verlag. | MR | Zbl

7. W. Browder, Algebraic $K$ -theory with coefficients $ℤ / p$ , LNM vol. 657 (1978), Springer-Verlag | MR | Zbl

8. M. Bökstedt, Topological Hochschild homology, Topology (to appear)

9. M. Bökstedt, Topological Hochschild homology of $ℤ$ and $ℤ / p$ ., Ann. of Math. (to appear).

10. M. Bökstedt, G. Carlsson, R. Cohen, T. Goodwillie, W. C Hsiang, I. Madsen, On the Algebraic $K$ -theory of simply connected $(i)$ spaces, Preprint, Aarhus (1991) | Zbl

11. M. Bökstedt, W.-C. Hsiang, I Madsen, The cyclotomic trace and algebraic $K$ -theory, Invent. Math (1993) | MR | Zbl

12. G. Carlsson, Equivariant stable homotopy and Segal's Burnside ring conjecture, Ann of Math. vol. 120, (1984), 189-224 | MR | Zbl | DOI

13. H. Cartan, S. Eilenberg, Homological Algebra, Princeton University Press (1956) | MR | Zbl

14. T. Tom Dieck, Orbittypen und äquivariante homologie II, Arch. Math. 26 (1975), 650-662 | MR | Zbl | DOI

15. T. Tom Dieck, Transformation groups and representation theory, LNM vol. 766 (1979), Springer-Verlag | MR | Zbl

16. T. Goodwillie, Calculus II, Analytic functors, $K$ -theory (to appear) | MR | Zbl

17. T. Goodwillie, Notes on the cyclotomic trace (in preparation)

18. J. P. C. Greenlees, Representing Tate cohomology of G-spaces, Proc. Edinburgh Math. Soc. vol. 30 (1987), 435-443 | MR | Zbl | DOI

19. J. P. C. Greenlees, J. P May, Generalized Tate, Borel and coBorel Cohomology, Preprint, Univ. of Chicago (1992)

20. L. Hesselholt, Stable topological cyclic homology is topological Hochschild homology, Astérisque ibid (1994) | MR | Zbl | Numdam

21. L. Hesselholt, I. Madsen, The $S^{1}$ -Tate spectrum for J, Preprint No. 28, Aarhus University (1992), Bull. Mex. Mat. Soc. (to appear) | Zbl | MR

22. L. Hesselholt, I Madsen, Topological cyclic homology of the dual numbers over finite fields, Preprint Aarhus University (1993)

23. L. G. Lewis, J. P. May, M. Steinberger, Equivariant stable homotopy theory, LNM vol 1213, (1986) Springer-Verlag | MR | Zbl

24. J.-L. Loday, D. Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59, (1984), 565-591 | Zbl | EuDML | MR | DOI

25. I. Madsen, The cyclotomic trace in algebraic K-theory, Proceedings ECM, Paris (1992) | Zbl

26. I. Madsen, V. Snaith, J. Tornehave, Infinite loop maps in geometric topology, Proc. Camb. Phil. Soc, vol. 81 (1977), 399-429 | MR | Zbl | DOI

27. J. P. May, The geometry of iterated loop spaces, LNM vol. 271 (1972) Springer-Verlag | MR | Zbl

28. J. P. May, J.E Mcclure, A reduction of the Segal conjecture, CMS Conf. Proceedings vol. 2, Part 2 (1981) Providence, 209-222 | MR | Zbl

29. S. Mitchel, The Morava $K$ -theory of algebraic $K$ -theory spectra, $K$ -theory vol. 3 (1990), 607-626 | MR | Zbl

30. D. Quillen, On the cohomology and $K$ -theory of general linear groups over finite fields, Annals of Math. vol. 96 (1972), 552-586 | MR | Zbl | DOI

31. D. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. vol. 106 (1984), 351-414 | MR | Zbl | DOI

32. D. Ravenel, The Segal conjecture for cyclic groups and its consequences, Amer. J. Math. vol. 106 (1984), 415-446 | MR | Zbl | DOI

33. J. Rognes, Two lemmas on BU, Proc. Camb. Math. Soc. (to appear)

34. G. B. Segal, Categories and cohomology theories, Topology vol. 13 (1974), 293-312 | MR | Zbl | DOI

35. G. B. Segal, Equivariant stable homotopy theory, Proc ICM, Nice (1970), 59-63 | MR | Zbl

36. K. Shimakawa, Infinite loop $G$ -spaces associated to monoidal $G$ -graded categories, Publ. Res Inst. Math. Sci. vol. 25, No. 2 (1989), 239-262 | MR | Zbl | DOI

37. R. Woolfson, Hyper- $Γ$ -spaces and hyper spectra, Quart. J. Math. Oxford (2), 30 (1979), 229-255 | MR | Zbl | DOI

38. F. Waldhausen, Algebraic $K$ -theory of topological spaces I, Proc. symposia in Pure Mathmatics, vol 32 (1978), 35-60 AMS, Providence, Rhode Island | MR | Zbl | DOI

39. F. Waldhausen, Algebraic $K$ -theory of topological spaces II, LNM vol. 763 (1978), Springer-Verlag | MR | Zbl

40. F. Waldhausen, Algebraic $K$ -theory of spaces, a manifold approach. Current Trends in Algebraic Topology, CMS Conference Proceedings vol 2, Part 1 (1982), 141-184 | MR | Zbl

41. C. Kassel, La $K$ -theorie stable, Bull. Soc. Math. France, 110 (1982), 381-416. | MR | Zbl | EuDML | Numdam | DOI