Étale Cohomology , Lefschetz Theorems and Number of Points of Singular Varieties over Finite Fields

@inproceedings{Ghorpade2002taleC,
  title={{\'E}tale Cohomology , Lefschetz Theorems and Number of Points of Singular Varieties over Finite Fields},
  author={Sudhir R. Ghorpade and Gilles Lachaud},
  year={2002}
}
We prove a general inequality for estimating the number of points of arbitrary complete intersections over a finite field. This extends a result of Deligne for nonsingular complete intersections. For normal complete intersections, this inequality generalizes also the classical Lang-Weil inequality. Moreover, we prove the Lang-Weil inequality for affine as well as projective varieties with an explicit description and a bound for the constant appearing therein. We also prove a conjecture of Lang… CONTINUE READING