Algebraic & Geometric Topology Volume 12, issue 1 (2012)

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Motivic twisted $K$–theory

Markus Spitzweck and Paul Arne Østvær

Algebraic & Geometric Topology 12 (2012) 565–599

DOI: 10.2140/agt.2012.12.565

Bibliography

1	J F Adams, Stable homotopy and generalised homology, , Univ. of Chicago Press (1974) MR0402720
2	D W Anderson, L Hodgkin, The K–theory of Eilenberg–Mac Lane complexes, Topology 7 (1968) 317 MR0231369
3	M Ando, A J Blumberg, D Gepner, Twists of K–theory and TMF, from: "Superstrings, geometry, topology, and C∗–algebras" (editors R S Doran, G Friedman, J Rosenberg), Proc. Sympos. Pure Math. 81, Amer. Math. Soc. (2010) 27 MR2681757
4	M Atiyah, G Segal, Twisted K–theory, Ukr. Mat. Visn. 1 (2004) 287 MR2172633
5	M Atiyah, G Segal, Twisted K–theory and cohomology, from: "Inspired by S S Chern" (editor P A Griffiths), Nankai Tracts Math. 11, World Sci. Publ. (2006) 5 MR2307274
6	S Bloch, Algebraic cycles and higher K–theory, Adv. in Math. 61 (1986) 267 MR852815
7	S Bloch, S Lichtenbaum, A spectral sequence for motivic cohomology, K–theory Preprint Archives 0062 (1995)
8	P Bouwknegt, A L Carey, V Mathai, M K Murray, D Stevenson, Twisted K–theory and K–theory of bundle gerbes, Comm. Math. Phys. 228 (2002) 17 MR1911247
9	U Bunke, D Freed, T Schick, editors, Arbeitsgemeinschaft mit aktuellem Thema : twisted K–theory, Oberwolfach Rep. 3 (2006) 2757 MR2334223
10	D C Cisinski, F Deglise, Triangulated categories of mixed motives arXiv:0912.2110
11	P Donovan, M Karoubi, Graded Brauer groups and K–theory with local coefficients, Inst. Hautes Études Sci. Publ. Math. (1970) 5 MR0282363
12	D Dugger, D C Isaksen, Motivic cell structures, Algebr. Geom. Topol. 5 (2005) 615 MR2153114
13	B I Dundas, M Levine, P A Østvær, O Röndigs, V Voevodsky, Motivic homotopy theory, , Springer (2007) MR2334212
14	B I Dundas, O Röndigs, P A Østvær, Motivic functors, Doc. Math. 8 (2003) 489 MR2029171
15	D S Freed, M J Hopkins, T Teleman, Loop groups and twisted K–theory I arXiv:0711.1906
16	E M Friedlander, A Suslin, The spectral sequence relating algebraic K–theory to motivic cohomology, Ann. Sci. École Norm. Sup. 35 (2002) 773 MR1949356
17	D Gepner, V Snaith, On the motivic spectra representing algebraic cobordism and algebraic K–theory, Doc. Math. 14 (2009) 359 MR2540697
18	D R Grayson, The motivic spectral sequence, from: "Handbook of K–theory. Vol. 1, 2" (editors E M Friedlander, D R Grayson), Springer (2005) 39 MR2181820
19	A Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. (1967) 361 MR0238860
20	J J Gutiérrez, O Röndigs, M Spitzweck, P A Østvær, Motivic slices and colored operads arXiv:1012.3301
21	J Hornbostel, Preorientations of the derived motivic multiplicative group arXiv:1005.4546
22	M Hovey, Homotopy theory of comodules over a Hopf algebroid, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 261 MR2066503
23	M Hovey, N Strickland, Comodules and Landweber exact homology theories, Adv. Math. 192 (2005) 427 MR2128706
24	P Hu, On the Picard group of the stable 𝔸¹–homotopy category, Topology 44 (2005) 609 MR2122218
25	J F Jardine, Motivic symmetric spectra, Doc. Math. 5 (2000) 445 MR1787949
26	M Karoubi, Twisted K–theory—old and new, from: "K–theory and noncommutative geometry" (editors G Cortiñas, J Cuntz, M Karoubi, R Nest, C A Weibel), EMS Ser. Congr. Rep., Eur. Math. Soc. (2008) 117 MR2513335
27	M Khorami, A universal coefficient theorem for twisted K–theory, J. Topol. 4 (2011) 535 MR2832567
28	M Levine, The homotopy coniveau tower, J. Topol. 1 (2008) 217 MR2365658
29	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
30	J P May, J Sigurdsson, Parametrized homotopy theory, 132, Amer. Math. Soc. (2006) MR2271789
31	F Morel, On the motivic π₀ of the sphere spectrum, from: "Axiomatic, enriched and motivic homotopy theory" (editor J P C Greenlees), NATO Sci. Ser. II Math. Phys. Chem. 131, Kluwer (2004) 219 MR2061856
32	N Naumann, M Spitzweck, P A Østvær, Chern classes, K–theory and Landweber exactness over nonregular base schemes, from: "Motives and algebraic cycles" (editors R de Jeu, J D Lewis), Fields Inst. Commun. 56, Amer. Math. Soc. (2009) 307 MR2562464
33	N Naumann, M Spitzweck, P A Østvær, Motivic Landweber exactness, Doc. Math. 14 (2009) 551 MR2565902
34	P Pelaez, Multiplicative properties of the slice filtration, 335, Soc. Math. France (2011) MR2807904
35	D Quillen, On the cohomology and K–theory of the general linear groups over a finite field, Ann. of Math. 96 (1972) 552 MR0315016
36	D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic Press (1986) MR860042
37	D C Ravenel, W S Wilson, The Hopf ring for complex cobordism, J. Pure Appl. Algebra 9 (1977) 241 MR0448337
38	O Röndigs, P A Østvær, Motives and modules over motivic cohomology, C. R. Math. Acad. Sci. Paris 342 (2006) 751 MR2227753
39	O Röndigs, P A Østvær, Modules over motivic cohomology, Adv. Math. 219 (2008) 689 MR2435654
40	O Röndigs, M Spitzweck, P A Østvær, Motivic strict ring models for K–theory, Proc. Amer. Math. Soc. 138 (2010) 3509 MR2661551
41	J Rosenberg, Continuous-trace algebras from the bundle theoretic point of view, J. Austral. Math. Soc. Ser. A 47 (1989) 368 MR1018964
42	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. 80 (2000) 491 MR1734325
43	M Spitzweck, Relations between slices and quotients of the algebraic cobordism spectrum, Homology, Homotopy Appl. 12 (2010) 335 MR2771593
44	M Spitzweck, P A Østvær, The Bott inverted infinite projective space is homotopy algebraic K–theory, Bull. Lond. Math. Soc. 41 (2009) 281 MR2496504
45	A Suslin, On the Grayson spectral sequence, Tr. Mat. Inst. Steklova 241 (2003) 218 MR2024054
46	A Suslin, V Voevodsky, Bloch–Kato conjecture and motivic cohomology with finite coefficients, from: "The arithmetic and geometry of algebraic cycles (Banff, AB, 1998)" (editors B B Gordon, J D Lewis, S Müller-Stach, S Saito, N Yui), NATO Sci. Ser. C Math. Phys. Sci. 548, Kluwer (2000) 117 MR1744945
47	J L Tu, P Xu, C Laurent-Gengoux, Twisted K–theory of differentiable stacks, Ann. Sci. École Norm. Sup. 37 (2004) 841 MR2119241
48	V Voevodsky, A¹–homotopy theory, from: "Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998)" (1998) 579 MR1648048
49	V Voevodsky, Open problems in the motivic stable homotopy theory. I, from: "Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998)", Int. Press Lect. Ser. 3, Int. Press, Somerville, MA (2002) 3 MR1977582
50	V Voevodsky, A possible new approach to the motivic spectral sequence for algebraic K–theory, from: "Recent progress in homotopy theory (Baltimore, MD, 2000)" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 371 MR1890744
51	V Voevodsky, On the zero slice of the sphere spectrum, Tr. Mat. Inst. Steklova 246 (2004) 106 MR2101286
52	V Voevodsky, O Röndigs, P A Østvær, Voevodsky’s Nordfjordeid lectures : motivic homotopy theory, from: "Motivic homotopy theory", Universitext, Springer (2007) 147 MR2334215
53	M E Walker, Chern classes for twisted K–theory, J. Pure Appl. Algebra 206 (2006) 153 MR2220087
54	E Witten, D-branes and K–theory, J. High Energy Phys. (1998) MR1674715