Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DISTRIBUTION OF VALUES OF FUNCTIONS OVER FINITE FIELDS

  • Chae, Hi-Joon (Department of Mathematics Education, Hongil University)
  • Published : 2004.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

Given a function on a scheme over a finite field, we can count the number of rational points of the scheme having the same values. We show that if the function, viewed as a morphism to the affine line, is proper and its higher direct image sheaves are tamely ramified at the infinity then the values are uniformly distributed up to some degree.

Keywords

References

  1. P. Deligne, La conjecture de Weil, II, Publ. Math. IHES 52 (1980), 137–252
  2. P. Deligne, Le formalisme des cycles evanescents, in Groupes de Monodromie en Geometrie Algebrique, Seminaire de Geometrie Algebrique 7 II, by P. Deligne and N. Katz, Lecture Notes in Math. 340 (1973), 82–115
  3. J. Denef and F. Loeser, Weights of exponential sums, intersection cohomology and Newton polyhedra, Invent. Math. 106 (1991), 275–294
  4. A. Grothendieck, Expose I, in Groupes de Monodromie en Geometrie Algebrique, Seminaire de Geometrie Algebrique 7 I, by A. Grothendieck, M. Raynaud and D. S. Rim, Lecture Notes in Math. 288 (1972), 1–24
  5. N. Katz, Sommes exponentielles, Asterisque 79 (1980)
  6. N. Katz and G. Laumon, Transformation de Fourier et majoration de sommes exponentielles, Publ. Math. IHES 62 (1985), 145–202
  7. M. Raynaud, Revetements de la droite affine en caracteristique p > 0 et conjecture dAbhyankar, Invent. Math. 116 (1994), 425–462