Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Topological Hochschild homology of number rings

Author(s): Ayelet Lindenstrauss; Ib Madsen
Journal: Trans. Amer. Math. Soc. 352 (2000), 2179-2204.
MSC (2000): Primary 19D55; Secondary 13D03, 19D50, 55Q52
Posted: February 16, 2000
MathSciNet review: 1707702
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We calculate an explicit formula for the topological Hochschild homology of a discrete valuation ring of characteristic zero with finite residue field. From this we deduce the topological Hochschild homology of global number rings.

References:

[B]
M. Bökstedt, Topological Hochschild homology, preprint (Bielefeld).
[B1]
M. Bökstedt, Topological Hochschild homology of $\mathbf{Z}$ and $\mathbf{Z}/p$, preprint (Bielefeld).
[BM]
M. Bökstedt, I. Madsen, Algebraic K-theory of local number fields: the unramified case, in Prospects in Topology (Princeton, 1994), Ann. of Math. Stud., vol. 139, Princeton Univ. Press, Princeton, NJ, 1995, pp. 28-57. MR 97e:19004
[Br]
L. Breen, Extensions du groupe additif, Publ. Math. I.H.E.S. 48 (1978) 39-123. MR 81f:14011
[Bro]
W. Browder, Torsion in $H$-spaces, Annals of Math. 74 (1961) 24-51. MR 23:A2201
[Brun]
M. Brun, Spectral sequences for topological Hochschild homology, Thesis, Aarhus University, 1997.
[Brun1]
M. Brun, Topological Hochschild homology of $Z/p^n$, J. Pure Appl. Algebra (to appear).
[BMMS]
R. R. Bruner, J. P. May, J. E. McClure, M. Steinberger, $H_\infty$-ring spectra and their applications, Lecture Notes in Mathematics 1176, Springer-Verlag, 1980. MR 88e:55001
[BAG]
Buenos Aires Cyclic Homology Group, Cyclic homology of algebras with one generator, K-Theory 5 (1991) 51-68. MR 93b:19002
[CLM]
F. R. Cohen, T. J. Lada, J. P. May, The Homology of Iterated Loop Spaces, Springer LNM 533, 1976. MR 55:9096
[DM]
B. Dundas, R. McCarthy, Stable K-theory and topological Hochschild homology, Annals of Math. 140 (1994) 685-689. MR 96e:19005a,b
[DM1]
B. Dundas, R. McCarthy, Topological Hochschild homology of ring functors and exact categories, J. Pure Appl. Algebra 109 (1996) 231-294. MR 97i:19001
[EKMM]
A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, Rings, Modules and Algebras in Stable Homotopy Theory, AMS Mathematical Surveys and Monographs vol. 47, 1997. MR 97a:55006
[FP]
V. Franjou, T. Pirashvili, On Mac Lane cohomology for the ring of integers, Topology 37 (1998) 109-114. MR 98h:19002
[HM]
L. Hesselholt, I. Madsen, On the K-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1996) 29-101. MR 97i:19002
[JP]
M. Jibladze, T. Pirashvili, Cohomology of algebraic theories, J. of Algebra 137 (1991) 253-296. MR 92f:18005
[K]
C. Kassel, La K-theorie stable, Bull. Soc. Math. France 110 (1982) 381-416. MR 84f:18018
[L]
A. Lindenstrauss, Topological Hochschild homology of extensions of $\mathbf{Z}/p\mathbf{Z}$ by polynomials, and of $\mathbf{Z}[x]/(x^n)$ and $\mathbf{Z}[x]/(x^n-1)$, K-Theory 10, 239-265, 1996. MR 98e:19001
[L1]
A. Lindenstrauss, The topological Hochschild homology of the Gaussian integers, Amer. J. Math. 118 (1996) 1011-1036. MR 98b:19002
[L2]
A. Lindenstrauss, A relative spectral sequence for topological Hochschild homology of spectra, J. Pure Appl. Algebra (to appear).
[Mac]
S. Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics 5, Springer-Verlag, 1971. MR 50:7275
[M]
I. Madsen, Algebraic K-theory and traces, in Current Developments in Mathematics, 191-321, International Press (1996). MR 98g:19004
[M1]
I. Madsen, Higher torsion in $SG$ and $BSG$, Math. Z. 143 (1975) 55-80. MR 51:11503
[May]
J. P. May, $E_\infty$ ring spaces and $E_\infty$ ring spectra, Lecture Notes in Mathematics 577, Springer-Verlag, 1977. MR 58:13008
[May1]
J. P. May, Simplicial Objects in Algebraic Topology, D. Van Nostrand Company, Inc., 1967. MR 36:5942
[PW]
T. Pirashvili, F. Waldhausen, Mac Lane homology and topological Hochschild homology, J. Pure Appl. Algebra 82 (1992) 81-98. MR 93k:16016
[Q]
D. Quillen, Homotopical Algebra, Lecture Notes in Mathematics 43, Springer-Verlag, 1967. MR 36:6480
[S]
J-P. Serre, Local Fields, Graduate Texts in Mathematics 67, Springer-Verlag, 1979. MR 82e:12016 2

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 19D55, 13D03, 19D50, 55Q52

Retrieve articles in all Journals with MSC (2000): 19D55, 13D03, 19D50, 55Q52

Additional Information:

Ayelet Lindenstrauss
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: ayelet@math.indiana.edu

Ib Madsen
Affiliation: Department of Mathematics, Aarhus University, DK-8000 Aarhus, Denmark
Email: imadsen@imf.au.dk

DOI: 10.1090/S0002-9947-00-02611-8
PII: S 0002-9947(00)02611-8
Received by editor(s): December 18, 1997
Posted: February 16, 2000
Copyright of article: Copyright 2000, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia