Geometry & Topology Volume 21, issue 6 (2017)

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The nilpotence theorem for the algebraic $K$–theory of the sphere spectrum

Andrew J Blumberg and Michael A Mandell

Geometry & Topology 21 (2017) 3453–3466

DOI: 10.2140/gt.2017.21.3453

Bibliography

1	P Balmer, The spectrum of prime ideals in tensor triangulated categories, J. Reine Angew. Math. 588 (2005) 149 MR2196732
2	P Balmer, Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings, Algebr. Geom. Topol. 10 (2010) 1521 MR2661535
3	P Báyer, J Neukirch, On values of zeta functions and l–adic Euler characteristics, Invent. Math. 50 (1978) 35 MR516603
4	H S Bergsaker, J Rognes, Homology operations in the topological cyclic homology of a point, Geom. Topol. 14 (2010) 735 MR2602850
5	A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic K–theory, Geom. Topol. 17 (2013) 733 MR3070515
6	A J Blumberg, D Gepner, G Tabuada, Uniqueness of the multiplicative cyclotomic trace, Adv. Math. 260 (2014) 191 MR3209352
7	A J Blumberg, M A Mandell, Algebraic K–theory and abstract homotopy theory, Adv. Math. 226 (2011) 3760 MR2764905
8	A J Blumberg, M A Mandell, Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories, preprint (2014) arXiv:1111.4003v3
9	M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic K–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
10	M Bökstedt, I Madsen, Topological cyclic homology of the integers, from: "K–theory" (editors C Kassel, J L Loday, N Schappacher), Astérisque 226, Soc. Math. France (1994) 57 MR1317117
11	A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR0387496
12	A K Bousfield, The localization of spectra with respect to homology, Topology 18 (1979) 257 MR551009
13	B I Dundas, Relative K–theory and topological cyclic homology, Acta Math. 179 (1997) 223 MR1607556
14	W G Dwyer, Twisted homological stability for general linear groups, Ann. of Math. 111 (1980) 239 MR569072
15	W G Dwyer, S A Mitchell, On the K–theory spectrum of a ring of algebraic integers, K-Theory 14 (1998) 201 MR1633505
16	B Ferrero, L C Washington, The Iwasawa invariant μ_p vanishes for abelian number fields, Ann. of Math. 109 (1979) 377 MR528968
17	T Geisser, The cyclotomic trace map and values of zeta functions, from: "Algebra and number theory" (editor R Tandon), Hindustan Book Agency (2005) 211 MR2193354
18	R Greenberg, On p–adic L–functions and cyclotomic fields, Nagoya Math. J. 56 (1975) 61 MR0360536
19	L Hesselholt, Algebraic K–theory and the p–adic L–function, unpublished notes
20	L Hesselholt, I Madsen, On the K–theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997) 29 MR1410465
21	M J Hopkins, Global methods in homotopy theory, from: "Homotopy theory" (editors E Rees, J D S Jones), London Math. Soc. Lecture Note Ser. 117, Cambridge Univ. Press (1987) 73 MR932260
22	N Kitchloo, J Morava, The stable symplectic category and a conjecture of Kontsevich, preprint (2012) arXiv:1212.6905
23	B Mazur, A Wiles, Class fields of abelian extensions of Q, Invent. Math. 76 (1984) 179 MR742853
24	J Morava, Homotopy-theoretically enriched categories of noncommutative motives, Res. Math. Sci. 2 (2015) MR3355473
25	A Neeman, The chromatic tower for D(R), Topology 31 (1992) 519 MR1174255
26	D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
27	D Quillen, Finite generation of the groups K_i of rings of algebraic integers, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 179 MR0349812
28	J Rognes, The Hatcher–Waldhausen map is a spectrum map, Math. Ann. 299 (1994) 529 MR1282230
29	J Rognes, Two-primary algebraic K–theory of pointed spaces, Topology 41 (2002) 873 MR1923990
30	J Rognes, The smooth Whitehead spectrum of a point at odd regular primes, Geom. Topol. 7 (2003) 155 MR1988283
31	J Rognes, C Weibel, Two-primary algebraic K–theory of rings of integers in number fields, J. Amer. Math. Soc. 13 (2000) 1 MR1697095
32	C Soulé, K–théorie des anneaux d’entiers de corps de nombres et cohomologie étale, Invent. Math. 55 (1979) 251 MR553999
33	J Tate, Duality theorems in Galois cohomology over number fields, from: "Proc. Internat. Congr. Mathematicians, I" (editor V Stenström), Inst. Mittag-Leffler (1963) 288 MR0175892
34	R W Thomason, Algebraic K–theory and étale cohomology, Ann. Sci. École Norm. Sup. 18 (1985) 437 MR826102
35	R W Thomason, The classification of triangulated subcategories, Compositio Math. 105 (1997) 1 MR1436741
36	F Waldhausen, Algebraic K–theory of spaces, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796
37	F Waldhausen, B Jahren, J Rognes, Spaces of PL manifolds and categories of simple maps, 186, Princeton Univ. Press (2013) MR3202834
38	L C Washington, Introduction to cyclotomic fields, 83, Springer (1997) MR1421575
39	C A Weibel, The K–book : an introduction to algebraic K-theory, 145, Amer. Math. Soc. (2013) MR3076731
40	M Weiss, B Williams, Automorphisms of manifolds, from: "Surveys on surgery theory, II" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 149, Princeton Univ. Press (2001) 165 MR1818774