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FULTON’S TRACE FORMULA

where the product on the right is taken over the closed points of x, and the equality follows by Galois theory. Z(X, t) is the generating function for the number of effective zero-cycles on X defined over Fq; its logarithmic derivative is the generating function for the number of Fqk -rational points of X. Grothendieck defines `-adic cohomology groups Hi(XFq ,Q`) satisfying the following beautiful identity: Theorem 1 (Grothendieck).