Torsion algebraic cycles and complex cobordism

Totaro, Burt¹

¹ Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, Illinois 60637

Journal of the American Mathematical Society, Tome 10 (1997) no. 2, pp. 467-493

Détail

DOI : 10.1090/S0894-0347-97-00232-4

Bibliographie

[1] Adams, J. F. Stable homotopy and generalised homology 1974

[2] Atiyah, M. F. The Grothendieck ring in geometry and topology 1963 442 446

[3] Atiyah, M. F., Hirzebruch, F. Analytic cycles on complex manifolds Topology 1962 25 45

[4] Classification of irregular varieties 1992

[5] Baum, Paul, Fulton, William, Macpherson, Robert Riemann-Roch for singular varieties Inst. Hautes Études Sci. Publ. Math. 1975 101 145

[6] Bloch, Spencer Algebraic cycles and values of 𝐿-functions. II Duke Math. J. 1985 379 397

[7] Colliot-Thã©Lã¨Ne, Jean-Louis Cycles algébriques de torsion et 𝐾-théorie algébrique 1993 1 49

[8] Colliot-Thã©Lã¨Ne, Jean-Louis, Sansuc, Jean-Jacques Quelques gammes sur les formes quadratiques J. Algebra 1983 449 467

[9] Conner, P. E., Smith, Larry On the complex bordism of finite complexes Inst. Hautes Études Sci. Publ. Math. 1969 117 221

[10] Conner, P. E., Smith, Larry On the complex bordism of finite complexes. II J. Differential Geometry 1971/72 135 174

[11] Fulton, William Intersection theory 1984

[12] Griffiths, Phillip A. On the periods of certain rational integrals. I, II Ann. of Math. (2) 1969

[13] Harada, Masana, Kono, Akira On the integral cohomology of extraspecial 2-groups J. Pure Appl. Algebra 1987 215 219

[14] Hartshorne, Robin Equivalence relations on algebraic cycles and subvarieties of small codimension 1973 129 164

[15] Hironaka, Heisuke Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II Ann. of Math. (2) 1964

[16] Hirzebruch, F. Topological methods in algebraic geometry 1966

[17] Inoue, Kouichi The Brown-Peterson cohomology of 𝐵𝑆𝑂(6) J. Math. Kyoto Univ. 1992 655 666

[18] Johnson, David Copeland, Wilson, W. Stephen Projective dimension and Brown-Peterson homology Topology 1973 327 353

[19] Kono, Akira, Yagita, Nobuaki Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups Trans. Amer. Math. Soc. 1993 781 798

[20] Landweber, Peter S. Coherence, flatness and cobordism of classifying spaces 1970 256 269

[21] Landweber, Peter S. Elements of infinite filtration in complex cobordism Math. Scand. 1972 223 226

[22] Merkur′Ev, A. S., Suslin, A. A. 𝐾-cohomology of Severi-Brauer varieties and the norm residue homomorphism Izv. Akad. Nauk SSSR Ser. Mat. 1982

[23] Milnor, John The Steenrod algebra and its dual Ann. of Math. (2) 1958 150 171

[24] Milnor, J. On the cobordism ring Ω* and a complex analogue. I Amer. J. Math. 1960 505 521

[25] Milnor, J. On axiomatic homology theory Pacific J. Math. 1962 337 341

[26] Milnor, John W., Stasheff, James D. Characteristic classes 1974

[27] Nori, Madhav V. Algebraic cycles and Hodge-theoretic connectivity Invent. Math. 1993 349 373

[28] Novikov, S. P. Homotopy properties of Thom complexes Mat. Sb. (N.S.) 1962 407 442

[29] Paranjape, Kapil H. Cohomological and cycle-theoretic connectivity Ann. of Math. (2) 1994 641 660

[30] Parimala, R., Suresh, V. Zero-cycles on quadric fibrations: finiteness theorems and the cycle map Invent. Math. 1995 83 117

[31] Quillen, Daniel On the formal group laws of unoriented and complex cobordism theory Bull. Amer. Math. Soc. 1969 1293 1298

[32] Quillen, Daniel Elementary proofs of some results of cobordism theory using Steenrod operations Advances in Math. 1971

[33] Quillen, Daniel The 𝑚𝑜𝑑 2 cohomology rings of extra-special 2-groups and the spinor groups Math. Ann. 1971 197 212

[34] Rojtman, A. A. The torsion of the group of 0-cycles modulo rational equivalence Ann. of Math. (2) 1980 553 569

[35] Schoen, Chad On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field Ann. Sci. École Norm. Sup. (4) 1995 1 50

[36] Serre, Jean-Pierre Sur la topologie des variétés algébriques en caractéristique 𝑝 1958 24 53

[37] Smith, Larry On realizing complex bordism modules. Applications to the stable homotopy of spheres Amer. J. Math. 1970 793 856

[38] Stong, Robert E. Notes on cobordism theory 1968

[39] Wilson, W. Stephen The Ω-spectrum for Brown-Peterson cohomology. II Amer. J. Math. 1975 101 123