Zeta-Functions of Varieties Over Finite Fields at s=1

  • Stephen Lichtenbaum
Part of the Progress in Mathematics book series (PM, volume 35)

Abstract

Let κ be a finite field of cardinality q = p . Let \(\overline \kappa \) be a fixed algebraic closure of κ. Let X be a smooth projective algebraic variety of dimension d over κ such that \(\overline X = X \times \overline \kappa \) is connected.

Keywords

Tate 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [De 1]
    Deligne, P. La conjecture de Weil, I. Publ. Math. I.H.B.S. 43 (1974), 273–307.MathSciNetGoogle Scholar
  2. [G]
    Gabber, O. Sur la torsion dans la cohomologie l-adique d’une variété (to appear).Google Scholar
  3. [K]
    Kaplansky, I. Infinite Abelian Groups, University of Michigan Press, Ann Arbor (1954).Google Scholar
  4. [Ml]
    Milne, J.S. On a conjecture of Artin and Tate, Ann of Math. 102 (1975), 517–533.MathSciNetMATHCrossRefGoogle Scholar
  5. [M2]
    Milne, J.S. Etale Cohomology, Princeton University Press, Princeton, (1980).Google Scholar
  6. [Mu]
    Mumford, D. Abelian Varieties, Oxford University Press, London (1970).MATHGoogle Scholar
  7. [T1]
    Tate, J. On a conjecture of Birch and Swinnerton-Dyer and a geometric analogue. Seminaire Bourbaki no. 306, 1965–66, W.A. Benjamin Inc. (1966).Google Scholar
  8. [T2]
    Tate, J. Algebraic cycles and poles of zeta-functions. Arithmetic Algebraic Geometry, Harper and Row, New York, (1965).Google Scholar
  9. [Z]
    Zarchin, Yu. G. The Brauer group of abelian varieties over finite fields, (in Russian) Izv. Akad. Nauk. USSR 46 (1980), 211–243. Received June 30, 1982 Partially supported by N.S.F. grantsGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Stephen Lichtenbaum
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

Personalised recommendations