Algebraic & Geometric Topology Volume 15, issue 2 (2015)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Semitopologization in motivic homotopy theory and applications

Amalendu Krishna and Jinhyun Park

Algebraic & Geometric Topology 15 (2015) 823–861

DOI: 10.2140/agt.2015.15.823

Bibliography

1	S Bloch, S Lichtenbaum, A spectral sequence for motivic cohomology, preprint
2	A K Bousfield, E M Friedlander, Homotopy theory of $\Gamma $–spaces, spectra and bisimplicial sets, from: "Geometric applications of homotopy theory, II", Lecture Notes in Math. 658, Springer (1978) 80 MR513569
3	C Chu, Morphic cohomology and singular cohomology of motives over the complex numbers, Topology Appl. 156 (2009) 2812 MR2556038
4	E M Friedlander, C Haesemeyer, M E Walker, Techniques, computations and conjectures for semitopological $K\!$–theory, Math. Ann. 330 (2004) 759 MR2102312
5	E M Friedlander, H B Lawson Jr., A theory of algebraic cocycles, Ann. of Math. 136 (1992) 361 MR1185123
6	E M Friedlander, A Suslin, The spectral sequence relating algebraic $K\!$–theory to motivic cohomology, Ann. Sci. École Norm. Sup. 35 (2002) 773 MR1949356
7	E M Friedlander, V Voevodsky, Bivariant cycle cohomology, from: "Cycles, transfers and motivic homology theories", Ann. of Math. Stud. 143, Princeton Univ. Press (2000) 138 MR1764201
8	E M Friedlander, M E Walker, Comparing $K\!$–theories for complex varieties, Amer. J. Math. 123 (2001) 779 MR1854111
9	E M Friedlander, M E Walker, Semitopological $K\!$–theory using function complexes, Topology 41 (2002) 591 MR1910042
10	E M Friedlander, M E Walker, Rational isomorphisms between $K\!$–theories and cohomology theories, Invent. Math. 154 (2003) 1 MR2004456
11	E M Friedlander, M E Walker, Semitopological $K\!$–theory, from: "Handbook of $K\!$–theory: Vol. 1, 2" (editors E M Friedlander, D R Grayson), Springer (2005) 877 MR2181835
12	P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Math. 174, Birkhäuser (1999) MR1711612
13	J B Heller, Semitopological cobordism for complex varieties, PhD Thesis, Northwestern University (2006)
14	P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003) MR1944041
15	M Hovey, Spectra and symmetric spectra in general model categories, J. Pure Appl. Algebra 165 (2001) 63 MR1860878
16	M Hoyois, From algebraic cobordism to motivic cohomology (2012) arXiv:1210.7182v3
17	J F Jardine, Generalized étale cohomology theories, Progress in Math. 146, Birkhäuser (1997) MR1437604
18	J F Jardine, Motivic symmetric spectra, Doc. Math. 5 (2000) 445 MR1787949
19	J F Jardine, The $K\!$–theory presheaf of spectra, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16 (2009) 151 MR2544389
20	Y Kim, Motivic symmetric ring spectrum representing algebraic $K\!$–theory, PhD Thesis, University of Illinois at Urbana-Champaign (2010)
21	A Krishna, J Park, Algebraic cobordism theory attached to algebraic equivalence, J. $K\!$–Theory 11 (2013) 73 MR3034284
22	T Lawson, Motivic homotopy: Notes from the lectures by M Hopkins, week $8$
23	M Levine, The homotopy coniveau tower, J. Topol. 1 (2008) 217 MR2365658
24	M Levine, Comparison of cobordism theories, J. Algebra 322 (2009) 3291 MR2567421
25	M Levine, F Morel, Algebraic cobordism, Springer (2007) MR2286826
26	S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
27	C Mazza, V Voevodsky, C Weibel, Lecture notes on motivic cohomology, Clay Math. Monogr. 2, Amer. Math. Soc. (2006) MR2242284
28	J McCleary, A user's guide to spectral sequences, Cambridge Studies in Advanced Math. 58, Cambridge Univ. Press (2001) MR1793722
29	S A Mitchell, Hypercohomology spectra and Thomason's descent theorem, from: "Algebraic $K\!$–theory" (editor V P Snaith), Fields Inst. Commun. 16, Amer. Math. Soc. (1997) 221 MR1466977
30	F Morel, The stable $\mathbb{A}^1$–connectivity theorems, $K\!$–Theory 35 (2005) 1 MR2240215
31	F Morel, $\mathbb A^1$–algebraic topology over a field, Lecture Notes in Math. 2052, Springer (2012) MR2934577
32	F Morel, V Voevodsky, $\mathbb{A}^1$–homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. (1999) 45 MR1813224
33	N Naumann, M Spitzweck, P A Østvær, Motivic Landweber exactness, Doc. Math. 14 (2009) 551 MR2565902
34	P A Østvær, O Röndigs, V Voevodsky, Voevodsky's Nordfjordeid lectures: Motivic homotopy theory, from: "Motivic homotopy theory", Springer (2007) 147 MR2334215
35	I Panin, Oriented cohomology theories of algebraic varieties, $K\!$–Theory 30 (2003) 265 MR2064242
36	O Röndigs, P A Østvær, Modules over motivic cohomology, Adv. Math. 219 (2008) 689 MR2435654
37	M Spitzweck, Relations between slices and quotients of the algebraic cobordism spectrum, Homology, Homotopy Appl. 12 (2010) 335 MR2771593
38	M Spitzweck, Slices of motivic Landweber spectra, J. $K\!$–Theory 9 (2012) 103 MR2887201
39	A Suslin, V Voevodsky, Relative cycles and Chow sheaves, from: "Cycles, transfers and motivic homology theories", Ann. of Math. Stud. 143, Princeton Univ. Press (2000) 10 MR1764199
40	R W Thomason, T Trobaugh, Higher algebraic $K\!$–theory of schemes and of derived categories, from: "The Grothendieck Festschrift, Vol. III" (editors P Cartier, L Illusie, N M Katz, G Laumon, K A Ribet), Progr. Math. 88, Birkhäuser (1990) 247 MR1106918
41	V Voevodsky, $\mathbb{A}^1$–homotopy theory, from: "Proc. of the International Congress of Math., Vol. I", Doc. Math. (1998) 579 MR1648048
42	V Voevodsky, On the zero slice of the sphere spectrum, Tr. Mat. Inst. Steklova 246 (2004) 106 MR2101286