On the zeta function of a projective complete intersection

Details On the zeta function of a projective complete intersection On the zeta function of a projective complete intersection

2006-10-06

arxiv.org/abs/math/0610230v1

Mathematics

Algebraic Geometry

24 pages, no figures

Scientific paper

We compute a basis for the p-adic Dwork cohomology of a smooth complete intersection in projective space over a finite field and use it to give p-adic estimates for the action of Frobenius on this cohomology. In particular, we prove that the Newton polygon of the characteristic polynomial of Frobenius lies on or above the associated Hodge polygon. This result was first proved by B. Mazur using crystalline cohomology.

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