Zero cycles and the number of generators of an ideal

Spencer Bloch; M. Pavaman Murthy; Lucien Szpiro

Mémoires de la Société Mathématique de France (1989)

  • Volume: 38, page 51-74
  • ISSN: 0249-633X

How to cite


Bloch, Spencer, Murthy, M. Pavaman, and Szpiro, Lucien. "Zero cycles and the number of generators of an ideal." Mémoires de la Société Mathématique de France 38 (1989): 51-74. <>.

author = {Bloch, Spencer, Murthy, M. Pavaman, Szpiro, Lucien},
journal = {Mémoires de la Société Mathématique de France},
keywords = {set theoretic intersections; embedding; Chow zero cycles},
language = {eng},
pages = {51-74},
publisher = {Société mathématique de France},
title = {Zero cycles and the number of generators of an ideal},
url = {},
volume = {38},
year = {1989},

AU - Bloch, Spencer
AU - Murthy, M. Pavaman
AU - Szpiro, Lucien
TI - Zero cycles and the number of generators of an ideal
JO - Mémoires de la Société Mathématique de France
PY - 1989
PB - Société mathématique de France
VL - 38
SP - 51
EP - 74
LA - eng
KW - set theoretic intersections; embedding; Chow zero cycles
UR -
ER -


  1. [Ba] H. BASS, Algebraic K-theory, Benjamin, New York, 1968. Zbl0174.30302MR40 #2736
  2. [Bl] S. BLOCH, Some elementary theorems about algebraic cycles on abelian varieties, Inventiones Math. 37 (1976), 215-228. Zbl0371.14007MR55 #2892
  3. [Bo] M. BORATYNSKI, On a conormal module of smooth set-theoretic complete intersections, Trans. Amer. Math. Soc. 296 (1986). Zbl0608.14036MR88b:14038
  4. [Fu] W. FULTON, Intersection Theory, Springer-Verlag, 1984. Zbl0541.14005MR85k:14004
  5. [Go] J.-E. GOODMAN, Affine open subsets of algebraic varieties and ample divisors, Ann. of Math. 89 (1969), 168-183. Zbl0159.50504MR39 #4170
  6. [Le] M. LEVINE, Zero cycles and K-theory on singular varieties, Algebraic Geometry Bowdoin 1985, Proc. Symp. in Pure Math. 46 (1987), 451-462. Zbl0635.14007MR89h:14005
  7. [Ly] G. LYUBEZNIK, The number of equations needed to define an algebraic set, (preprint). 
  8. [Mi] J.S. MILNES, Zero cycles on algebraic varieties in non-zero characteristic : Roitman's theorem, Compositio Math. 47 (1982), 271-287. Zbl0506.14006
  9. [MK1] N. MOHAN KUMAR, On two conjectures about polynomial rings, Inventiones Math. 46 (1978), 225-236. Zbl0395.13009MR80c:13010
  10. [MK2] N. MOHAN KUMAR, Complete intersection, J. Math. Kyoto Univ. 17 (1977), 533-538. Zbl0384.14016MR57 #12540
  11. [MK3] N. MOHAN KUMAR, Set-theoretic generation of ideals, (preprint). 
  12. [MKM] N. MOHAN KUMAR and M.P. MURTHY, Algebraic cycles and vector bundles over affine three-folds, Ann. of Math. 116 (1982), 579-591. Zbl0519.14009MR84d:14006
  13. [MKMR] N. MOHAN KUMAR, M.P. MURTHY and A. ROY, A cancellation theorem for projective modules over finitely generated rings, to appear in "Algebraic Geometry and Commutative Algebra in Honor of Masayashi Nagata", 1987. Zbl0696.13006
  14. [Mu] D. MUMFORD, Rational equivalence of 0-cycles on surfaces, J. Math. Kyoto Univ. 9 (1969), 195-204. Zbl0184.46603MR40 #2673
  15. [Mu1] M.P. MURTHY, Complete intersections, Conference on Commutative Algebra, Queen's Papers Pure Appl. Math. 42 (1975), 196-211. Zbl0354.14015MR53 #453
  16. [Mu2] M.P. MURTHY, Generators for certain ideals in regular rings of dimension three, Comment. Math. Helv. 47 (1972), 179-184. Zbl0251.13006MR47 #8517
  17. [Mu3] M.P. MURTHY, Affine varieties as complete intersections, Intl. Symp. on Algebraic Geometry, Kyoto (1977), 231-236. Zbl0418.14028MR81i:14034
  18. [Mu4] M.P. MURTHY, Zero cycles, splitting of projective modules and number of generators of a module, (preprint). 
  19. [Mu5] M.P. MURTHY, Zero cycles and projective modules, (in preparation). 
  20. [MS] M.P. MURTHY and R.G. SWAN, Vector bundles over affine surfaces, Inventiones Math. 36 (1966), 125-165. Zbl0362.14006MR55 #12724
  21. [Ro1] A.A. ROITMAN, On Г-equivalence of zero-dimensional cycles, Math. USSR Sbornik 15 (1971), 555-567. Zbl0259.14002MR44 #6701
  22. [Ro2] A.A. ROITMAN, Rational equivalence of zero-cycles, Math. USSR Sbornik 18 (1972), 571-588. Zbl0273.14001MR48 #6109
  23. [Ro3] A.A. ROITMAN, The torsion of the group of 0-cycles modulo rational equivalence, Ann. of Math. 111 (1980), 553-569. Zbl0504.14006MR81g:14003
  24. [Sr] V. SRINIVAS, Torsion 0-cycles on affine varieties in characteristic p, (preprint). 
  25. [Su] A.A. SUSLIN, A cancellation theorem for projective modules over algebras, Soviet Math. Dokl. 18 (1977), 1281-1284. Zbl0395.13003MR57 #5986
  26. [Sw] R.G. SWAN, A cancellation theorem for projective modules in the metastable range, Inventiones Math. 27 (1974), 23-43. Zbl0297.14003MR51 #12856
  27. [Sz] L. SZPIRO, Equations defining space curves, Published for Tata Institute oof Fundamental Research by Springer-Verlag (1979). Zbl0442.14010MR82d:14017
  28. [We] E. WEISS, Algebraic Number Theory, Mc Graw-Hill, 1963. Zbl0115.03601MR28 #3021

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.