@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},
pages = {45--143},
year = {1999},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {90},
zbl = {0983.14007},
mrnumber = {1813224},
language = {en},
url = {https://www.numdam.org/item/PMIHES_1999__90__45_0/}
}
TY - JOUR AU - Morel, Fabien AU - Voevodsky, Vladimir TI - $A^1$-homotopy theory of schemes JO - Publications Mathématiques de l'IHÉS PY - 1999 SP - 45 EP - 143 VL - 90 PB - Institut des Hautes Etudes Scientifiques UR - https://www.numdam.org/item/PMIHES_1999__90__45_0/ LA - en ID - PMIHES_1999__90__45_0 ER -
Morel, Fabien; Voevodsky, Vladimir. $A^1$-homotopy theory of schemes. Publications Mathématiques de l'IHÉS, Tome 90 (1999), pp. 45-143. https://www.numdam.org/item/PMIHES_1999__90__45_0/
[1] , On the joins of Hensel rings, Advances in Math. 7 (1971), 282-296. | Zbl | MR
[2] and , Homotopy theory of Γ-spaces, spectra, and bisimplicial sets, Lecture Notes in Math. 658 (1978), 80-130. | Zbl | MR
[3] and , Homotopy limits, completions and localizations, Lecture Notes in Math. 304 (1972), Springer-Verlag. | Zbl | MR
[4] , Constructions of factorization systems in categories, J. Pure Appl. Alg. 9 (1977), 207-220. | Zbl | MR
[5] , Homotopical localizations of spaces, American J. of Math. 119 (1997), 1321-1354. | Zbl | MR
[6] , Abstract homotopy theory and generalized sheaf cohomology, Trans. A.M.S., vol. 186 (1973), 419-458. | Zbl | MR
[7] and , Algebraic K-theory and generalized sheaf cohomology, Lecture Notes in Math. 341 (1973), 266-292. | Zbl | MR
[8] , K-theory of tetrahedra, J. Algebra (1979), 129-144. | Zbl | MR
[9] , , and , Model categories and general abstract homotopy theory, In preparation.
[10] , Cellular Spaces, Null Spaces and Homotopy Localizations, Lecture Notes in Math. 1622 (1973), Springer-Verlag. | Zbl | MR
[11] and , Cellular structures in topology, Cambridge, Cambridge Univ. Press, 1990. | Zbl | MR
[12] and , Filtrations on the homology of algebraic varieties, vol. 529 of Memoir of the AMS, AMS, Providence, RI, 1994. | Zbl | MR
[13] , and , Théorie des topos et cohomologie étale des schémas (SGA 4), Lecture Notes in Math. 269, 270, 305 (1972-1973), Heidelberg, Springer.
[14] and , Étude globale élémentaire de quelques classes de morphismes (EGA 2), Publ. Math. IHES 8, 1961. | Numdam
[15] and , Étude locale des schémas et des morphismes de schémas (EGA 4), Publ. Math. IHES 20, 24, 28, 32, 1964-1967. | Zbl | Numdam
[16] , and , Symmetric spectra, Preprint, 1996. | Zbl
[17] , Simplicial objects in a Grothendieck topos, Contemporary Math. 55(1) (1986), 193-239. | Zbl | MR
[18] , Simplicial presheaves, J. Pure Appl. Algebra 47 (1987), 35-87. | Zbl | MR
[19] , Stable homotopy theory of simplicial presheaves, Canadian J. Math. 39(3) (1987), 733-747. | Zbl | MR
[20] , Letter to A. Grothendieck (1984).
[21] , Categories for working mathematician, vol. 5 of Graduate texts in Mathematics, Springer-Verlag, 1971. | Zbl | MR
[22] , Simplicial objects in algebraic topology, Van Nostrand, 1968. | Zbl
[23] , Cosimplicial homotopies, Proc. AMS 108(1) (1990), 9-17. | Zbl | MR
[24] , étale Cohomology, Princeton Math. Studies 33, Princeton University Press (1980). | Zbl | MR
[25] , 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. | Zbl | MR
[26] , Homotopical algebra, Lecture Notes in Math. 43 (1973), Berlin, Springer-Verlag. | Zbl | MR
[27] , Classifying spaces and spectral sequences, Publ. Math. IHES 34 (1968), 105-112. | Zbl | MR | Numdam
[28] , and , Singular homology of abstract algebraic varieties, Invent. math. 123 (1996), 61-94. | Zbl | MR
[29] , Algebraic K-theory and étale cohomology, Ann. Sci. ENS 18 (1985), 437-552. | Zbl | MR | Numdam
[30] and , Higher algebraic K-theory of schemes and of derived categories, In The Grothendieck festchrift, vol. 3 (1990), 247-436, Boston, Birkhauser. | MR
[31] , Homology of schemes, Selecta Mathematica, New Series 2(1) (1996), 111-153. | Zbl | MR
[32] , The A1-homotopy theory, Proceedings of the international congress of mathematicians, Berlin, 1998. | Zbl | MR
[33] , Homotopy K-theory, Contemp. Math. 83 (1987), 461-488. Theorem. | Zbl | MR






