A 1 -homotopy theory of schemes
Morel, Fabien ; Voevodsky, Vladimir
Publications Mathématiques de l'IHÉS, Tome 90 (1999), p. 45-143 / Harvested from Numdam
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@article{PMIHES_1999__90__45_0,
     author = {Morel, Fabien and Voevodsky, Vladimir},
     title = {$A^1$-homotopy theory of schemes},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {90},
     year = {1999},
     pages = {45-143},
     mrnumber = {2002f:14029},
     zbl = {0983.14007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1999__90__45_0}
}

Morel, Fabien; Voevodsky, Vladimir. $A^1$-homotopy theory of schemes. Publications Mathématiques de l'IHÉS, Tome 90 (1999) pp. 45-143. http://gdmltest.u-ga.fr/item/PMIHES_1999__90__45_0/

[1] M. Artin, On the joins of Hensel rings, Advances in Math. 7 (1971), 282-296. | MR 44 #6690 | Zbl 0242.13021

[2] A. K. Bousfield and E. M. Friedlander, Homotopy theory of Γ-spaces, spectra, and bisimplicial sets, Lecture Notes in Math. 658 (1978), 80-130. | MR 80e:55021 | Zbl 0405.55021

[3] A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304 (1972), Springer-Verlag. | MR 51 #1825 | Zbl 0259.55004

[4] A. K. Bousfield, Constructions of factorization systems in categories, J. Pure Appl. Alg. 9 (1977), 207-220. | MR 57 #17648 | Zbl 0361.18001

[5] A. K. Bousfield, Homotopical localizations of spaces, American J. of Math. 119 (1997), 1321-1354. | MR 98m:55009 | Zbl 0886.55011

[6] K. S. Brown, Abstract homotopy theory and generalized sheaf cohomology, Trans. A.M.S., vol. 186 (1973), 419-458. | MR 49 #6220 | Zbl 0245.55007

[7] K. S. Brown and S. M. Gersten, Algebraic K-theory and generalized sheaf cohomology, Lecture Notes in Math. 341 (1973), 266-292. | MR 50 #442 | Zbl 0291.18017

[8] B. Dayton, K-theory of tetrahedra, J. Algebra (1979), 129-144. | MR 80e:18007 | Zbl 0402.18011

[9] W. G. Dwyer, P. S. Hirschhorn, and D. M. Kan, Model categories and general abstract homotopy theory, In preparation.

[10] E. Dror-Farjoun, Cellular Spaces, Null Spaces and Homotopy Localizations, Lecture Notes in Math. 1622 (1973), Springer-Verlag. | MR 98f:55010 | Zbl 0842.55001

[11] R. Fritsch and R. A. Piccinini, Cellular structures in topology, Cambridge, Cambridge Univ. Press, 1990. | MR 92d:55001 | Zbl 0837.55001

[12] E. M. Friedlander and B. Mazur, Filtrations on the homology of algebraic varieties, vol. 529 of Memoir of the AMS, AMS, Providence, RI, 1994. | MR 95a:14023 | Zbl 0841.14019

[13] A. Grothendieck, M. Artin and J.-L. Verdier, Théorie des topos et cohomologie étale des schémas (SGA 4), Lecture Notes in Math. 269, 270, 305 (1972-1973), Heidelberg, Springer.

[14] A. Grothendieck and J. Dieudonné, Étude globale élémentaire de quelques classes de morphismes (EGA 2), Publ. Math. IHES 8, 1961. | Numdam

[15] A. Grothendieck and J. Dieudonné, Étude locale des schémas et des morphismes de schémas (EGA 4), Publ. Math. IHES 20, 24, 28, 32, 1964-1967. | Numdam | Zbl 0136.15901

[16] M. Hovey, B. Shipley and J. Smith, Symmetric spectra, Preprint, 1996. | Zbl 0931.55006

[17] J. F. Jardine, Simplicial objects in a Grothendieck topos, Contemporary Math. 55(1) (1986), 193-239. | MR 88g:18008 | Zbl 0606.18006

[18] J. F. Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987), 35-87. | MR 88j:18005 | Zbl 0624.18007

[19] J. F. Jardine, Stable homotopy theory of simplicial presheaves, Canadian J. Math. 39(3) (1987), 733-747. | MR 88j:18004 | Zbl 0645.18006

[20] A. Joyal, Letter to A. Grothendieck (1984).

[21] S. Maclane, Categories for working mathematician, vol. 5 of Graduate texts in Mathematics, Springer-Verlag, 1971. | MR 50 #7275 | Zbl 0232.18001

[22] J. P. May, Simplicial objects in algebraic topology, Van Nostrand, 1968. | Zbl 0165.26004

[23] J. P. Meyer, Cosimplicial homotopies, Proc. AMS 108(1) (1990), 9-17. | MR 90d:55016 | Zbl 0683.18012

[24] J. S. Milne, étale Cohomology, Princeton Math. Studies 33, Princeton University Press (1980). | MR 81j:14002 | Zbl 0433.14012

[25] Y. Nisnevich, The completely decomposed topology on schemes and associated descent spectral sequences in algebraic K-theory. In Algebraic K-theory: connections with geometry and topology, p. 241-342. Kluwer Acad. Publ., Dordrecht, 1989. | MR 91c:19004 | Zbl 0715.14009

[26] D. Quillen, Homotopical algebra, Lecture Notes in Math. 43 (1973), Berlin, Springer-Verlag. | MR 36 #6480 | Zbl 0168.20903

[27] G. B. Segal, Classifying spaces and spectral sequences, Publ. Math. IHES 34 (1968), 105-112. | Numdam | MR 38 #718 | Zbl 0199.26404

[28] A. Suslin, and V. Voevodsky, Singular homology of abstract algebraic varieties, Invent. math. 123 (1996), 61-94. | MR 97e:14030 | Zbl 0896.55002

[29] R. Thomason, Algebraic K-theory and étale cohomology, Ann. Sci. ENS 18 (1985), 437-552. | Numdam | MR 87k:14016 | Zbl 0596.14012

[30] R. Thomason and T. Trobaugh, Higher algebraic K-theory of schemes and of derived categories, In The Grothendieck festchrift, vol. 3 (1990), 247-436, Boston, Birkhauser. | MR 92f:19001

[31] V. Voevodsky, Homology of schemes, Selecta Mathematica, New Series 2(1) (1996), 111-153. | MR 98c:14016 | Zbl 0871.14016

[32] V. Voevodsky, The A1-homotopy theory, Proceedings of the international congress of mathematicians, Berlin, 1998. | MR 99j:14018 | Zbl 0907.19002

[33] C. Weibel, Homotopy K-theory, Contemp. Math. 83 (1987), 461-488. Theorem. | MR 90d:18006 | Zbl 0669.18007