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Milne, J. S.

Zero cycles on algebraic varieties in nonzero characteristic: Rojtman’s theorem. (English) Zbl 0506.14006

Compos. Math. 47, 271-287 (1982).
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Cited in 1 Review
Cited in 25 Documents

MSC:

14C25 Algebraic cycles
14C15 (Equivariant) Chow groups and rings; motives
14G15 Finite ground fields in algebraic geometry
14F35 Homotopy theory and fundamental groups in algebraic geometry

Keywords:

nonzero characteristic; Chow group of zero cycles; Albanese variety; Quillen K-sheaves; surface over finite field; fundamental group

Citations:

Zbl 0334.14010; Zbl 0504.14006
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Full Text: Numdam EuDML

References:

[1] S. Bloch : Torsion algebraic cycles and a theorem of Roitman . Comp. Math. 39 (1979) 107-127. · Zbl 0463.14002
[2] S. Bloch : Lectures on algebraic cycles . Duke Math. Series IV. Duke University, 1980. · Zbl 0436.14003
[3] P. Cartier : Questions de rationalité des diviseurs en géometrie algébrique . Bull. Soc. Math. France 86 (1958) 177-251. · Zbl 0091.33501 · doi:10.24033/bsmf.1503
[4] R. Hartshorne : Ample subvarieties of algebraic varieties . Lecture Notes in Math. 156. Springer, Heidelberg, 1970. · Zbl 0208.48901 · doi:10.1007/BFb0067839
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[6] L. Illusie : Complexe de De Rham-Witt et cohomologie cristalline . Ann. Sc. Ec. Norm. Sup. 12 (1979) 501-661. · Zbl 0436.14007 · doi:10.24033/asens.1374
[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. · Zbl 0463.12006
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[9] S. Lang : On quasi algebraic closure . Ann. of Math. 55 (1952) 373-390. · Zbl 0046.26202 · doi:10.2307/1969785
[10] J. Milne : On the conjectures of Birch and Swinnerton-Dyer . Thesis, Harvard University, 1967.
[11] J. Milne : Duality in the flat cohomology of a surface . Ann. Sc. Ec. Norm. Sup. 9 (1976) 171-202. · Zbl 0334.14010 · doi:10.24033/asens.1309
[12] J. Milne : Etale cohomology . Princeton Univ. Press, Princeton, 1980. · Zbl 0433.14012
[13] F. Oort : Commutative group schemes . Lecture Notes in Math. 15. Springer, Heidelberg, 1966. · Zbl 0216.05603 · doi:10.1007/BFb0097479
[14] A Paršin : Abelian coverings of arithmetic schemes . Soviet Math Dokl 19 (1978) 1438-1442. · Zbl 0443.12006
[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. · Zbl 0292.18004 · doi:10.1007/BFb0067053
[16] A. Roitman : The torsion of the group of O-cycles modulo rational equivalence . Ann. of Math. 111 (1980) 553-569. · Zbl 0504.14006 · doi:10.2307/1971109
[17] J.-P. Serre : Corps locaux . Hermann, Paris, 1962. · Zbl 0137.02601
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