Zero cycles on algebraic varieties in nonzero characteristic : Rojtman's theorem

J. S. Milne

Compositio Mathematica (1982)

  • Volume: 47, Issue: 3, page 271-287
  • ISSN: 0010-437X

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Milne, J. S.. "Zero cycles on algebraic varieties in nonzero characteristic : Rojtman's theorem." Compositio Mathematica 47.3 (1982): 271-287. <http://eudml.org/doc/89575>.

@article{Milne1982,
author = {Milne, J. S.},
journal = {Compositio Mathematica},
keywords = {nonzero characteristic; Chow group of zero cycles; Albanese variety; Quillen K-sheaves; surface over finite field; fundamental group},
language = {eng},
number = {3},
pages = {271-287},
publisher = {Martinus Nijhoff Publishers},
title = {Zero cycles on algebraic varieties in nonzero characteristic : Rojtman's theorem},
url = {http://eudml.org/doc/89575},
volume = {47},
year = {1982},
}

TY - JOUR
AU - Milne, J. S.
TI - Zero cycles on algebraic varieties in nonzero characteristic : Rojtman's theorem
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 47
IS - 3
SP - 271
EP - 287
LA - eng
KW - nonzero characteristic; Chow group of zero cycles; Albanese variety; Quillen K-sheaves; surface over finite field; fundamental group
UR - http://eudml.org/doc/89575
ER -

References

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  1. [1] S. Bloch: Torsion algebraic cycles and a theorem of Roitman. Comp. Math.39 (1979) 107-127. Zbl0463.14002MR539002
  2. [2] S. Bloch: Lectures on algebraic cycles. Duke Math. Series IV. Duke University, 1980. Zbl0436.14003MR558224
  3. [3] P. Cartier: Questions de rationalité des diviseurs en géometrie algébrique. Bull. Soc. Math. France86 (1958) 177-251. Zbl0091.33501MR106223
  4. [4] R. Hartshorne: Ample subvarieties of algebraic varieties. Lecture Notes in Math.156. Springer, Heidelberg, 1970. Zbl0208.48901MR282977
  5. [5] R. Hartshorne: Algebraic geometry. Springer, Heidelberg, 1977. Zbl0367.14001MR463157
  6. [6] L. Illusie: Complexe de De Rham-Witt et cohomologie cristalline. Ann. Sc. Ec. Norm. Sup.12 (1979) 501-661. Zbl0436.14007MR565469
  7. [7] K. Kato: A generalization of local class field theory by using K-groups I. J. Fac. Sci., Univ. of Tokyo, Sec. IA 26 (1979) 303-376 II ibid., 27 (1980) 603-683. Zbl0463.12006MR550688
  8. [8] K. Kato: Galois cohomology of complete discrete valuation fields. Proc. Oberwolfach Conference on Algebraic K-theory, June 1980. Lecture Notes in Math.Springer, to appear. Zbl0506.12022MR689394
  9. [9] S. Lang: On quasi algebraic closure. Ann. of Math.55 (1952) 373-390. Zbl0046.26202MR46388
  10. [10] J. Milne: On the conjectures of Birch and Swinnerton-Dyer. Thesis, Harvard University, 1967. 
  11. [11] J. Milne: Duality in the flat cohomology of a surface. Ann. Sc. Ec. Norm. Sup.9 (1976) 171-202. Zbl0334.14010MR460331
  12. [12] J. Milne: Etale cohomology. Princeton Univ. Press, Princeton, 1980. Zbl0433.14012MR559531
  13. [13] F. Oort: Commutative group schemes. Lecture Notes in Math. 15. Springer, Heidelberg, 1966. Zbl0216.05603MR213365
  14. [14] A Paršin: Abelian coverings of arithmetic schemes. Soviet Math Dokl19 (1978) 1438-1442. Zbl0443.12006
  15. [15] D. Quillen: Higher algebraic K-theory I. Proc. of Seattle Conference on K-theory, pp. 85-147. Lecture Notes in Math. 341, Springer, Heidelberg, 1973. Zbl0292.18004MR338129
  16. [16] A. Roitman: The torsion of the group of O-cycles modulo rational equivalence. Ann. of Math.111 (1980) 553-569. Zbl0504.14006MR577137
  17. [17] J.-P. Serre: Corps locaux. Hermann, Paris, 1962. Zbl0137.02601MR354618

Citations in EuDML Documents

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  1. Spencer Bloch, M. Pavaman Murthy, Lucien Szpiro, Zero cycles and the number of generators of an ideal
  2. Marc N. Levine, V. Srinivas, Zero cycles on certain singular elliptic surfaces
  3. Michel Gros, Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique
  4. J. S. Milne, Motivic cohomology and values of zeta functions
  5. Antoine Chambert-loir, Points rationnels et groupes fondamentaux : applications de la cohomologie p -adique
  6. Chad Schoen, On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field

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