Zeta-Functions of Varieties Over Finite Fields at s=1
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.
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- [De 1]
- [G]Gabber, O. Sur la torsion dans la cohomologie l-adique d’une variété (to appear).Google Scholar
- [K]Kaplansky, I. Infinite Abelian Groups, University of Michigan Press, Ann Arbor (1954).Google Scholar
- [M2]Milne, J.S. Etale Cohomology, Princeton University Press, Princeton, (1980).Google Scholar
- [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
- [T2]Tate, J. Algebraic cycles and poles of zeta-functions. Arithmetic Algebraic Geometry, Harper and Row, New York, (1965).Google Scholar
- [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