2 . Points over Finite Fields and the Weil Conjectures
نویسنده
چکیده
In this chapter we will relate the topology of smooth projective varieties over the complex numbers with counting points over finite fields, via the Weil conjectures. If X is a variety defined over a finite field Fq, one can count its points over the various finite extensions of Fq; denote Nm = |X(Fmq )| (for instance, if X ⊂ AnFq is affine, given by equations f1, . . . , fk, then Nm = |{x ∈ Fmq | fi(x) = 0, ∀i}|). The local Weil zeta function of X,
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