Volume 23, issue 1 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29, 1 issue Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
The homotopy groups of the algebraic $K$–theory of the sphere spectrum

Andrew J Blumberg and Michael A Mandell

Geometry & Topology 23 (2019) 101–134
Bibliography
1 V Angeltveit, A Blumberg, T Gerhardt, M Hill, T Lawson, M Mandell, Topological cyclic homology via the norm, preprint (2014) arXiv:1401.5001
2 C Ausoni, B I Dundas, J Rognes, Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere, Doc. Math. 13 (2008) 795 MR2466184
3 A J Blumberg, M A Mandell, The nilpotence theorem for the algebraic K–theory of the sphere spectrum, Geom. Topol. 21 (2017) 3453 MR3692970
4 M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic K–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
5 M Bökstedt, I Madsen, Topological cyclic homology of the integers, from: "K–theory", Astérisque 226, Soc. Math. France (1994) 57 MR1317117
6 M Bökstedt, I Madsen, Algebraic K–theory of local number fields : the unramified case, from: "Prospects in topology" (editor F Quinn), Ann. of Math. Stud. 138, Princeton Univ. Press (1995) 28 MR1368652
7 A K Bousfield, The localization of spectra with respect to homology, Topology 18 (1979) 257 MR551009
8 B I Dundas, Relative K–theory and topological cyclic homology, Acta Math. 179 (1997) 223 MR1607556
9 W G Dwyer, E M Friedlander, Topological models for arithmetic, Topology 33 (1994) 1 MR1259512
10 W G Dwyer, S A Mitchell, On the K–theory spectrum of a ring of algebraic integers, K–Theory 14 (1998) 201 MR1633505
11 T G Goodwillie, Relative algebraic K–theory and cyclic homology, Ann. of Math. 124 (1986) 347 MR855300
12 L Hesselholt, I Madsen, On the K–theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997) 29 MR1410465
13 L Hesselholt, I Madsen, On the K–theory of local fields, Ann. of Math. 158 (2003) 1 MR1998478
14 J R Klein, J Rognes, The fiber of the linearization map A() K(), Topology 36 (1997) 829 MR1432423
15 M Kolster, T Nguyen Quang Do, V Fleckinger, Twisted S–units, p–adic class number formulas, and the Lichtenbaum conjectures, Duke Math. J. 84 (1996) 679 MR1408541
16 R Lee, R H Szczarba, The group K3(Z) is cyclic of order forty-eight, Ann. of Math. 104 (1976) 31 MR0442934
17 R Lee, R H Szczarba, On the torsion in K4() and K5(), Duke Math. J. 45 (1978) 101 MR0491893
18 I Madsen, Algebraic K–theory and traces, from: "Current developments in mathematics, 1995" (editors R Bott, M Hopkins, A Jaffe, I Singer, D Stroock, S T Yau), Int. (1994) 191 MR1474979
19 I Madsen, C Schlichtkrull, The circle transfer and K–theory, from: "Geometry and topology" (editors K Grove, I H Madsen, E K Pedersen), Contemp. Math. 258, Amer. Math. Soc. (2000) 307 MR1778114
20 B Mazur, A Wiles, Class fields of abelian extensions of , Invent. Math. 76 (1984) 179 MR742853
21 R McCarthy, Relative algebraic K–theory and topological cyclic homology, Acta Math. 179 (1997) 197 MR1607555
22 D C Ravenel, The Segal conjecture for cyclic groups and its consequences, Amer. J. Math. 106 (1984) 415 MR737779
23 D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
24 K A Ribet, A modular construction of unramified p–extensions of Q(μp), Invent. Math. 34 (1976) 151 MR0419403
25 J Riou, Algebraic K–theory, A1–homotopy and Riemann–Roch theorems, J. Topol. 3 (2010) 229 MR2651359
26 J Rognes, Characterizing connected K–theory by homotopy groups, Math. Proc. Cambridge Philos. Soc. 114 (1993) 99 MR1219917
27 J Rognes, K4() is the trivial group, Topology 39 (2000) 267 MR1722028
28 J Rognes, Two-primary algebraic K–theory of pointed spaces, Topology 41 (2002) 873 MR1923990
29 J Rognes, The smooth Whitehead spectrum of a point at odd regular primes, Geom. Topol. 7 (2003) 155 MR1988283
30 P Schneider, Über gewisse Galoiscohomologiegruppen, Math. Z. 168 (1979) 181 MR544704
31 R W Thomason, Algebraic K–theory and étale cohomology, Ann. Sci. École Norm. Sup. 18 (1985) 437 MR826102
32 F Waldhausen, Algebraic K–theory of spaces : a manifold approach, from: "Current trends in algebraic topology, I" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 141 MR686115
33 F Waldhausen, Algebraic K–theory of spaces, localization, and the chromatic filtration of stable homotopy, from: "Algebraic topology" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 173 MR764579
34 F Waldhausen, B Jahren, J Rognes, Spaces of PL manifolds and categories of simple maps, 186, Princeton Univ. Press (2013) MR3202834
35 L C Washington, Introduction to cyclotomic fields, 83, Springer (1997) MR1421575
36 C A Weibel, The K–book : an introduction to algebraic K–theory, 145, Amer. Math. Soc. (2013) MR3076731