Duke Mathematical Journal

Roitman’s theorem for singular complex projective surfaces

L. Barbieri-Viale, C. Pedrini, and C. Weibel

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 84, Number 1 (1996), 155-190.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077243631

Digital Object Identifier
doi:10.1215/S0012-7094-96-08405-7

Mathematical Reviews number (MathSciNet)
MR1394751

Zentralblatt MATH identifier
0864.14026

Subjects
Primary: 14C35: Applications of methods of algebraic $K$-theory [See also 19Exx]
Secondary: 19E15: Algebraic cycles and motivic cohomology [See also 14C25, 14C35, 14F42] 19E20: Relations with cohomology theories [See also 14Fxx]

Citation

Barbieri-Viale, L.; Pedrini, C.; Weibel, C. Roitman’s theorem for singular complex projective surfaces. Duke Math. J. 84 (1996), no. 1, 155--190. doi:10.1215/S0012-7094-96-08405-7. https://projecteuclid.org/euclid.dmj/1077243631


Export citation

References

  • [1] M. Artin, A. Grothendieck, and J.-L. Verdier, Théorie des topos et cohomologie étale des schémas. Tome 3, Lecture Notes in Mathematics, vol. 305, Springer-Verlag, Berlin, 1973.
  • [2] L. Barbieri-Viale, Zero-cycles on singular varieties: torsion and Bloch's formula, J. Pure Appl. Algebra 78 (1992), no. 1, 1–13.
  • [3] L. Barbieri-Viale and V. Srinivas, On the Néron-Severi group of a singular variety, J. Reine Angew. Math. 435 (1993), 65–82.
  • [4] L. Barbieri-Viale and V. Srinivas, The Néron-Severi group and the mixed Hodge structure on $H\sp 2$. Appendix to: “On the Néron-Severi group of a singular variety”, J. Reine Angew. Math. 450 (1994), 37–42.
  • [5] H. Bass and J. Tate, The Milnor ring of a global field, Algebraic $K$-theory, II: “Classical” algebraic $K$-theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972), Springer, Berlin, 1973, 349–446. Lecture Notes in Math., Vol. 342.
  • [6] A. Beilinson, Higher regulators and values of $L$-functions, J. Soviet Math. 30 (1985), 2036–2070.
  • [7] K. Brown and S. Gersten, Algebraic $K$-theory as generalized sheaf cohomology, Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 266–292. Lecture Notes in Math., Vol. 341.
  • [8] A. Collino, Quillen's $K$-theory and algebraic cycles on singular varieties, Geometry today (Rome, 1984), Progr. Math., vol. 60, Birkhäuser Boston, Boston, MA, 1985, pp. 75–85.
  • [9] A. Collino, Torsion in the Chow group of codimension two: the case of varieties with isolated singularities, J. Pure Appl. Algebra 34 (1984), no. 2-3, 147–153.
  • [10] J.-L. Colliot-Thélène, Cycles algébriques de torsion et $K$-théorie algébrique, Arithmetic algebraic geometry (Trento, 1991) ed. E. Ballico, Lecture Notes in Math., vol. 1553, Springer-Verlag, Berlin, 1993, pp. 1–49.
  • [11] J.-L. Colliot-Thélène and W. Raskind, $\scr K\sb 2$-cohomology and the second Chow group, Math. Ann. 270 (1985), no. 2, 165–199.
  • [12]1 P. Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. (1971), no. 40, 5–57.
  • [12]2 P. Deligne, Théorie de Hodge. III, Inst. Hautes Études Sci. Publ. Math. (1974), no. 44, 5–77.
  • [13] H. Esnault, Une remarque sur la cohomologie du faisceau de Zariski de la $K$-théorie de Milnor sur une variété lisse complexe, Math. Z. 205 (1990), no. 3, 373–378.
  • [14] H. Esnault and E. Viehweg, Deligne-Beĭlinson cohomology, Beĭlinson's conjectures on special values of $L$-functions, Perspect. Math., vol. 4, Academic Press, Boston, MA, 1988, pp. 43–91.
  • [15] O. Gabber, $K$-theory of Henselian local rings and Henselian pairs, Algebraic $K$-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989), Contemp. Math., vol. 126, Amer. Math. Soc., Providence, RI, 1992, pp. 59–70.
  • [16] S. Geller and L. Roberts, Kahler differentials and excision for curves, J. Pure Appl. Algebra 17 (1980), no. 1, 85–112.
  • [17] S. Geller and C. Weibel, $K\sb1(A,\,B,\,I)$, J. Reine Angew. Math. 342 (1983), 12–34.
  • [18] H. Gillet, Riemann-Roch theorems for higher algebraic $K$-theory, Adv. in Math. 40 (1981), no. 3, 203–289.
  • [19] H. Gillet, On the $K$-theory of surfaces with multiple curves and a conjecture of Bloch, Duke Math. J. 51 (1984), no. 1, 195–233.
  • [20] H. Gillet, Deligne homology and Abel-Jacobi maps, Bull. Amer. Math. Soc. (N.S.) 10 (1984), no. 2, 285–288.
  • [21] J. Graham, Continuous symbols on fields of formal power series, Algebraic $K$-theory, II: “Classical” algebraic $K$-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 474–486. Lecture Notes in Math., Vol. 342.
  • [22] R. Hoobler, Étale cohomology of geometric local rings is Galois cohomology, to appear.
  • [23] J. F. Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987), no. 1, 35–87.
  • [24] M. Levine, Bloch's formula for singular surfaces, Topology 24 (1985), no. 2, 165–174.
  • [25] M. Levine, Torsion zero-cycles on singular varieties, Amer. J. Math. 107 (1985), no. 3, 737–757.
  • [26] M. Levine, Zero-cycles and $K$-theory on singular varieties, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 451–462.
  • [27] M. Levine and C. Weibel, Zero cycles and complete intersections on singular varieties, J. Reine Angew. Math. 359 (1985), 106–120.
  • [28] S. Lichtenbaum, The construction of weight-two arithmetic cohomology, Invent. Math. 88 (1987), no. 1, 183–215.
  • [29] J. Lipman, Rational singularities, with applications to algebraic surfaces and unique factorization, Inst. Hautes Études Sci. Publ. Math. (1969), no. 36, 195–279.
  • [30] J. P. May, Simplicial objects in algebraic topology, Van Nostrand Math. Stud., No. 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967.
  • [31] J. Milnor and J. Stasheff, Characteristic classes, Annals of Mathematics Studies, vol. 76, Princeton University Press, Princeton, N. J., 1974.
  • [32] D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. (1961), no. 9, 5–22.
  • [33] C. Pedrini and C. Weibel, $K$-theory and Chow groups on singular varieties, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 339–370.
  • [34] C. Pedrini and C. Weibel, Divisibility in the Chow group of zero-cycles on a singular surface, Astérisque (1994), no. 226, 10–11, 371–409.
  • [35] W. Raskind, On $K\sb 1$ of curves over global fields, Math. Ann. 288 (1990), no. 2, 179–193.
  • [36] A. A. Rojtman, The torsion of the group of $0$-cycles modulo rational equivalence, Ann. of Math. (2) 111 (1980), no. 3, 553–569.
  • [37] A. Suslin, On the $K$-theory of local fields, J. Pure Appl. Algebra 34 (1984), no. 2-3, 301–318.
  • [38] A. Suslin, Torsion in $K\sb 2$ of fields, $K$-Theory 1 (1987), no. 1, 5–29.
  • [39] R. Thomason and T. Trobaugh, Higher algebraic $K$-theory of schemes and of derived categories, The Grothendieck Festschrift, Vol. III, Progr. Math., vol. 88, Birkhäuser Boston, Boston, MA, 1990, pp. 247–435.
  • [40] C. Weibel, Mayer-Vietoris sequences and mod $p$ $K$-theory, Algebraic $K$-theory, Part I (Oberwolfach, 1980), Lecture Notes in Math., vol. 966, Springer, Berlin, 1982, pp. 390–407.
  • [41] C. Weibel, Étale Chern classes at the prime $2$, Algebraic $K$-theory and algebraic topology (Lake Louise, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 407, Kluwer Acad. Publ., Dordrecht, 1993, pp. 249–286.
  • [42] C. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994.