On the $K$-theory of surfaces with multiple curves and a conjecture of Bloch

previous :: next

On the $K$-theory of surfaces with multiple curves and a conjecture of Bloch

Henri Gillet

Source: Duke Math. J. Volume 51, Number 1 (1984), 195-233.

First Page: Show

Primary Subjects: 14C35

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

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077303675
Mathematical Reviews number (MathSciNet): MR744295
Zentralblatt MATH identifier: 0557.14003
Digital Object Identifier: doi:10.1215/S0012-7094-84-05111-1

back to Table of Contents

References

[1] H. Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968.

Mathematical Reviews (MathSciNet): MR40:2736

Zentralblatt MATH: 0174.30302

[2] A. A. Beĭ linson, Higher regulators and values of $L$-functions of curves, Funktsional. Anal. i Prilozhen. 14 (1980), no. 2, 46–47.

Mathematical Reviews (MathSciNet): MR81k:14020

Zentralblatt MATH: 0475.14015

[3] S. Bloch, $K\sb2$ of Artinian $Q$-algebras, with application to algebraic cycles, Comm. Algebra 3 (1975), 405–428.

Mathematical Reviews (MathSciNet): MR51:8108

Zentralblatt MATH: 0327.14002

Digital Object Identifier: doi:10.1080/00927877508822053

[4] S. Bloch, A. Kas, and D. Lieberman, Zero cycles on surfaces with $p\sbg=0$, Compositio Math. 33 (1976), no. 2, 135–145.

Mathematical Reviews (MathSciNet): MR55:8035

Zentralblatt MATH: 0337.14006

[5] S. Boch, Lecture Notes on Algebraic Cycles, Duke U. Lecture Notes in Math., vol. IV, 1979.

[6] S. Boch, Applications of the dilogarithm function in algebraic $K$-theory and algebraic geometry, Int'l. Symp. on Alg. Geometry, Kyoto, 1977, 103–114.

Zentralblatt MATH: 0416.18016

[7]¹ P. Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. (1971), no. 40, 5–57.

Mathematical Reviews (MathSciNet): MR58:16653a

Zentralblatt MATH: 0219.14007

Digital Object Identifier: doi:10.1007/BF02684692

[7]² P. Deligne, Théorie de Hodge. III, Inst. Hautes Études Sci. Publ. Math. (1974), no. 44, 5–77.

Mathematical Reviews (MathSciNet): MR58:16653b

Zentralblatt MATH: 0237.14003

Digital Object Identifier: doi:10.1007/BF02685881

[8] S. C. Geller and L. G. Roberts, The relationship between the Picard groups and $SK\sb1$ of some algebraic curves, J. Algebra 55 (1978), no. 2, 213–230.

Mathematical Reviews (MathSciNet): MR80a:14003

Zentralblatt MATH: 0409.14004

Digital Object Identifier: doi:10.1016/0021-8693(78)90218-1

[9] H. Gillet, Riemann-Roch theorems for higher algebraic $K$-Theory, Adv. in Math. 40 (1981), no. 3, 203–289.

Mathematical Reviews (MathSciNet): MR83m:14013

Zentralblatt MATH: 0478.14010

Digital Object Identifier: doi:10.1016/S0001-8708(81)80006-0

[10] H. Gillet, Comparison of $K$-theory spectral sequences, with applications, Algebraic $K$-theory, Evanston 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980), Lecture Notes in Math., vol. 854, Springer, Berlin, 1981, pp. 141–167.

Mathematical Reviews (MathSciNet): MR83a:14021

Zentralblatt MATH: 0478.14011

[11] D. Grayson, Higher algebraic $K$-theory. II (after Daniel Quillen), Algebraic $K$-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) ed. M. R. Stein, Springer, Berlin, 1976, 217–240. Lecture Notes in Math., Vol. 551.

Mathematical Reviews (MathSciNet): MR58:28137

Zentralblatt MATH: 0362.18015

[12] P. A. Griffiths, Some results on algebraic cycles on algebraic manifolds, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, London, 1969, Papers presented at the Bombay colloquium, pp. 93–191.

Mathematical Reviews (MathSciNet): MR41:1746

Zentralblatt MATH: 0206.49803

[13] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978.

Mathematical Reviews (MathSciNet): MR80b:14001

Zentralblatt MATH: 0408.14001

[14] A. Grothendieck, Revêtements étales et groupe fondamental, Springer-Verlag, Berlin, 1971.

Mathematical Reviews (MathSciNet): MR50:7129

Zentralblatt MATH: 0234.14002

[15] F. Keune, The relativization of $K\sb2$, J. Algebra 54 (1978), no. 1, 159–177.

Mathematical Reviews (MathSciNet): MR80a:18013

Zentralblatt MATH: 0403.18009

Digital Object Identifier: doi:10.1016/0021-8693(78)90024-8

[16] D. Lieberman, Intermediate Jacobians, Algebraic Geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math.) ed. F. Oort, Wolters-Noordhoff, Groningen, 1972, pp. 125–139.

Mathematical Reviews (MathSciNet): MR54:12790

Zentralblatt MATH: 0249.14015

[17] D. Ramakrishnan, A regulator for curves via the Heisenberg group, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 2, 191–195.

Mathematical Reviews (MathSciNet): MR82m:12008

Zentralblatt MATH: 0519.14011

Digital Object Identifier: doi:10.1090/S0273-0979-1981-14942-9

Project Euclid: euclid.bams/1183548299

[18] D. Mumford, Lectures on curves on an algebraic surface, Annals of Math. Studies, no. 59, Princeton University Press, Princeton, N.J., 1966.

Mathematical Reviews (MathSciNet): MR35:187

Zentralblatt MATH: 0187.42701

[19] D. Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85–147.

Mathematical Reviews (MathSciNet): MR49:2895

Zentralblatt MATH: 0292.18004

[20] J.-P. Serre, Groupes algébriques et corps de classes, Publications de l'institut de mathématique de l'université de Nancago, VII. Hermann, Paris, 1959.

Mathematical Reviews (MathSciNet): MR21:1973

Zentralblatt MATH: 0097.35604

[21] J. Stienstra, Deformations of the second Chow group, a $K$-theoretic approach, Thesis, Univ. of Utrecht, 1978.

[22] C. Traverso, Seminormality and Picard group, Ann. Scuola Norm. Sup. Pisa (3) 24 (1970), 585–595.

Mathematical Reviews (MathSciNet): MR43:3275

Zentralblatt MATH: 0205.50501

[23] K. S. Brown and S. M. Gersten, Algebraic $K$-theory as generalized sheaf cohomology, Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) ed. H. Bass, Lecture Notes in Math., vol. 304, Springer, Berlin, 1973, pp. 266–292.

Mathematical Reviews (MathSciNet): MR50:442

Zentralblatt MATH: 0291.18017

[24] C. Weibel, Private Communication.

[25] P. Barthelot, et al., Théorie des intersections et théorème de Riemann–Roch, Lecture Notes in Math., no. 225, Springer-Verlag, Berlin, 1971, SGA 6.

Mathematical Reviews (MathSciNet): MR50:7133

[26] D. Mumford, Rational equivalence of $0$-cycles on surfaces, J. Math. Kyoto Univ. 9 (1968), 195–204.

Mathematical Reviews (MathSciNet): MR40:2673

Zentralblatt MATH: 0184.46603

Project Euclid: euclid.kjm/1250523940

[27] S. Bloch, $K\rm \sb2$ and algebraic cycles, Ann. of Math. (2) 99 (1974), 349–379.

Mathematical Reviews (MathSciNet): MR49:7260

Zentralblatt MATH: 0298.14005

Digital Object Identifier: doi:10.2307/1970902

JSTOR: links.jstor.org

[28] A. A. Roitman, Rational equivalence of $0$-cycles, Math. USSR, Sb 4 (1972), no. 18, 571–588.

[29] J. A. Carlson, The obstruction to splitting a mixed Hodge structure over the integers, Preprint, Univ. of Utah, 1979.

[30] P. Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. (1974), no. 43, 273–307.

Mathematical Reviews (MathSciNet): MR49:5013

Zentralblatt MATH: 0287.14001

Digital Object Identifier: doi:10.1007/BF02684373

[31] F. El Zein and S. Zucker, Extendability of normal functions associated to algebraic cycles, Manuscript.

[32] S. Kleiman, Misconceptions about $K\sbx$, Enseign. Math. (2) 25 (1979), no. 3-4, 203–206 (1980).

Mathematical Reviews (MathSciNet): MR81e:14003

Zentralblatt MATH: 0432.14013

[33] A. Bousfield and D. Kan, Homotopy limits, Completions and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, Berlin, 1975.

Zentralblatt MATH: 0259.55004

Mathematical Reviews (MathSciNet): MR365573

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?