A vanishing theorem for Fano varieties in positive characteristic

Details A vanishing theorem for Fano varieties in positive characteristic A vanishing theorem for Fano varieties in positive characteristic

2002-01-20

arxiv.org/abs/math/0201183v3

Mathematics

Algebraic Geometry

A correct proof of the original vanishing theorem (mod torsion) has been given in the meanwhile by Esnault. This note strength

Scientific paper

We prove a Kodaira-type vanishing theorem for the Witt vector sheaf on a Fano
variety over a perfect field of characteristic p. As a corollary, we deduce
that the number of rational points on a Fano variety over a finite field with
q=p^n elements is congruent to 1 mod q. This refines a result of Esnault which
say that the number is congruent to 1 mod p.

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