ON THE ZETA-FUNCTION OF A COMPLETE INTERSECTION

In this article, we compute the p-adic Dwork cohomology of a smooth co mplete intersection in T-m x A(n) or p(N) over a finite field (where T -m is the m-torus). As an application, we prove the ''Katz Conjecture' ' (i.e., the assertion that the Newton polygon lies over the Hodge pol ygon) for such varieties. This result is new in the case of T-m x Ann. (The case of P-N is due to Mazur [14].)