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Zeta functions of algebraic cycles over finite fields

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References

  1. Bloch, S.: Lectures on algebraic cycles, Duke Unly, Math, Series, 1980

  2. Carlitz, L.: On factorizable polynomials in several indeterminates. Duke Math. J. 2, 660–670 (1936)

    Article  MATH  MathSciNet  Google Scholar 

  3. Carlitz, L.: The distribution of irreducible polynomials in several indeterminates. Illinois J. Math., 7, 371–375 (1963)

    MATH  MathSciNet  Google Scholar 

  4. Carlitz, L.: The distribution of irreducible polynomials in several indeterminates II. Canadian J. Math., 17, 261–166 (1965)

    MATH  Google Scholar 

  5. Chow, W.L., van der Waerden, B.L.: Zur Algebraischen Geometrie. IX, Math. Ann., 113, 692–704 (1936)

    Article  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  7. Cohen, S.D.: Further arithmetic functions in finite fields. Proc. Edinburgh Math. Soc. (Ser. 2), 16, 349–364 (1969)

    Article  MATH  Google Scholar 

  8. Deligne, P., Katz, N.M.: Groupes de Monodromie en Géométrie Algébrique. SGA II, Springer Lecture Notes, 340, 1973

  9. Dwork, B.: On the rationality of zeta functions. Amer. J. Math., 82, 631–648 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  10. Denef, J.: The rationality of Poincare series associated to thep-adic points on a variety. Invent. Math., 77, 1–23 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  11. Franke, J., Manin, Y.I., Tschinkel, Y.: Rational points of bounded height on Fano varieties. Invent. Math., 95, 421–436 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Friendlander, E.: Homology using Chow varieties. Bull. Amer. Math. Soc., 20, 49–53 (1989)

    Article  MathSciNet  Google Scholar 

  13. Fulton, W.: Intersection Theory. Berlin Heidelberg New York Tokyo: Springer 1984

    MATH  Google Scholar 

  14. Grothendieck, A.: Cohomologie Locale des Faisceaux Cohérents et Théorèmes de Lefschetz Locaux et Globaux. SGA 2, Noth-Holland, Amsterdam, 1968

    Google Scholar 

  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)

  16. Hartshorne, R.: Algebraic Geometry. Berlin Heidelberg New York, Springer 1977

    MATH  Google Scholar 

  17. Igusa, J.I.: Lectures on Forms of Higher Degree. Tata Inst. Fund. Research, Bombay, 1978

    MATH  Google Scholar 

  18. Lang, S., Néron, A.: Rational points of abelian varieties over function fields. Amer. J. Math., 81, 95–118 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lang, S.: Introduction to Algebraic Geometry. Addison-Wesley Publ. Comp. Inc., 1972

  20. Lawson, B.: Algebraic cycles and homotopy theory. Ann. Math., 129, 253–291 (1989)

    Article  MathSciNet  Google Scholar 

  21. Lidl, R., Niedereiter, H.: Finite Fields. Encycl. Math and Its Appl., Addison-Wesley Publ. Comp. Inc., 1983

  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)

  23. Koblitz N.:p-adic Number,p-adic Analysis and Zeta-functions. Graduate Texts in Math., Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  24. Koblitz, N.:p-adic Analysis: A Short Course on Recent Work. Cambridge University Press, 1980

  25. Kleiman, S.L.: Toward a numerical theory of ampleness. Ann. Math., 84, 293–344 (1966)

    Article  MathSciNet  Google Scholar 

  26. Mazur, B.: Frobenius and the Hodge filtration, Bull. Amer. Math. Soc., 78, 653–667 (1972)

    MATH  MathSciNet  Google Scholar 

  27. Monsky, P.:p-adic Analysis and Zeta Functions. Kinokuniya Book Store Cor. Ltd. Tokyo, 1970

    MATH  Google Scholar 

  28. Mumford, D.: Abelian Varieties. Oxford University Press, 1974

  29. Serre, J.P.: Quelques applications du théorème densité de Chebotarev. Publ. Math. IHES, 54, 123–201 (1981)

    MATH  Google Scholar 

  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. 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)

  32. Wan, D.: Hilbert sets and zeta functions over finite fields. Crelles Journal, to appear

  33. Weil, A.: Number of solutions of equations over finite fields Bull. Amer. Math. Soc. 55, 497–508 (1949)

    MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  35. Zariski, O.: Interprétations algébrico-géométriques du quatorzième problème de Hilbert. Bull. Soc. Math., 78, 155–168 (1954)

    MATH  MathSciNet  Google Scholar 

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Wan, D. Zeta functions of algebraic cycles over finite fields. Manuscripta Math 74, 413–444 (1992). https://doi.org/10.1007/BF02567679

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