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manuscripta mathematica

, Volume 74, Issue 1, pp 413–444 | Cite as

Zeta functions of algebraic cycles over finite fields

  • Daqing Wan
Article

Keywords

Zeta Function Finite Field Projective Variety Abelian Variety Irreducible Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bloch, S.: Lectures on algebraic cycles, Duke Unly, Math, Series, 1980Google Scholar
  2. 2.
    Carlitz, L.: On factorizable polynomials in several indeterminates. Duke Math. J. 2, 660–670 (1936)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Carlitz, L.: The distribution of irreducible polynomials in several indeterminates. Illinois J. Math., 7, 371–375 (1963)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Carlitz, L.: The distribution of irreducible polynomials in several indeterminates II. Canadian J. Math., 17, 261–166 (1965)zbMATHGoogle Scholar
  5. 5.
    Chow, W.L., van der Waerden, B.L.: Zur Algebraischen Geometrie. IX, Math. Ann., 113, 692–704 (1936)CrossRefzbMATHGoogle Scholar
  6. 6.
    Cohen, S.D.: The distribution of irreducible polynomials in several indeterminates over a finite field. Proc. Edinburgh Math. Soc. (Ser. 2), 16, 1–17 (1968)zbMATHGoogle Scholar
  7. 7.
    Cohen, S.D.: Further arithmetic functions in finite fields. Proc. Edinburgh Math. Soc. (Ser. 2), 16, 349–364 (1969)zbMATHCrossRefGoogle Scholar
  8. 8.
    Deligne, P., Katz, N.M.: Groupes de Monodromie en Géométrie Algébrique. SGA II, Springer Lecture Notes, 340, 1973Google Scholar
  9. 9.
    Dwork, B.: On the rationality of zeta functions. Amer. J. Math., 82, 631–648 (1960)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Denef, J.: The rationality of Poincare series associated to thep-adic points on a variety. Invent. Math., 77, 1–23 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Franke, J., Manin, Y.I., Tschinkel, Y.: Rational points of bounded height on Fano varieties. Invent. Math., 95, 421–436 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Friendlander, E.: Homology using Chow varieties. Bull. Amer. Math. Soc., 20, 49–53 (1989)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Fulton, W.: Intersection Theory. Berlin Heidelberg New York Tokyo: Springer 1984zbMATHGoogle Scholar
  14. 14.
    Grothendieck, A.: Cohomologie Locale des Faisceaux Cohérents et Théorèmes de Lefschetz Locaux et Globaux. SGA 2, Noth-Holland, Amsterdam, 1968Google Scholar
  15. 15.
    Hartshorne, R.: Equivalence relations on algebraic cycles and subvarieties of small codimension. In Algebraic Geometry, Arcata 1974, Amer. Math. Soc. Proc. Symp. Pure Math. 29, 129–164 (1975)Google Scholar
  16. 16.
    Hartshorne, R.: Algebraic Geometry. Berlin Heidelberg New York, Springer 1977zbMATHGoogle Scholar
  17. 17.
    Igusa, J.I.: Lectures on Forms of Higher Degree. Tata Inst. Fund. Research, Bombay, 1978zbMATHGoogle Scholar
  18. 18.
    Lang, S., Néron, A.: Rational points of abelian varieties over function fields. Amer. J. Math., 81, 95–118 (1959)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Lang, S.: Introduction to Algebraic Geometry. Addison-Wesley Publ. Comp. Inc., 1972Google Scholar
  20. 20.
    Lawson, B.: Algebraic cycles and homotopy theory. Ann. Math., 129, 253–291 (1989)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Lidl, R., Niedereiter, H.: Finite Fields. Encycl. Math and Its Appl., Addison-Wesley Publ. Comp. Inc., 1983Google Scholar
  22. 22.
    Lipman, J.: Unique factorization in complete local rings. In Algebraic Geometry, Arcata 1974, Amer. Math. Soc. Proc. Symp. Pure Math. 29, 531–546 (1975)Google Scholar
  23. 23.
    Koblitz N.:p-adic Number,p-adic Analysis and Zeta-functions. Graduate Texts in Math., Berlin Heidelberg New York: Springer 1977Google Scholar
  24. 24.
    Koblitz, N.:p-adic Analysis: A Short Course on Recent Work. Cambridge University Press, 1980Google Scholar
  25. 25.
    Kleiman, S.L.: Toward a numerical theory of ampleness. Ann. Math., 84, 293–344 (1966)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Mazur, B.: Frobenius and the Hodge filtration, Bull. Amer. Math. Soc., 78, 653–667 (1972)zbMATHMathSciNetGoogle Scholar
  27. 27.
    Monsky, P.:p-adic Analysis and Zeta Functions. Kinokuniya Book Store Cor. Ltd. Tokyo, 1970zbMATHGoogle Scholar
  28. 28.
    Mumford, D.: Abelian Varieties. Oxford University Press, 1974Google Scholar
  29. 29.
    Serre, J.P.: Quelques applications du théorème densité de Chebotarev. Publ. Math. IHES, 54, 123–201 (1981)zbMATHGoogle Scholar
  30. 30.
    Tate, J.: Algebraic cycles and poles of zeta functions. In Arithmetic Algebraic Geometry (Schilling, ed.), Harper and Row, New York, 93–110 (1965)Google Scholar
  31. 31.
    Tate, J.: On the conjecture of Birch and Swinnerton-Dyer and a geometric analog. In Dix Exposés sur la cohomologie des schémas, North Holland, 189–214 (1968)Google Scholar
  32. 32.
    Wan, D.: Hilbert sets and zeta functions over finite fields. Crelles Journal, to appearGoogle Scholar
  33. 33.
    Weil, A.: Number of solutions of equations over finite fields Bull. Amer. Math. Soc. 55, 497–508 (1949)zbMATHMathSciNetGoogle Scholar
  34. 34.
    Zariski, O.: The theorem of Riemann-Roch for high multiple of an effective divisor on an algebraic surface. Ann. Math., 76, 560–615 (1962)CrossRefMathSciNetGoogle Scholar
  35. 35.
    Zariski, O.: Interprétations algébrico-géométriques du quatorzième problème de Hilbert. Bull. Soc. Math., 78, 155–168 (1954)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Daqing Wan
    • 1
  1. 1.Department of Mathematical SciencesUniversity of Nevada at Las VegasLas VegasUSA

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