This preprint was accepted November 11, 1998
Contact: I. PANIN and A. SMIRNOV
ABSTRACT: It is considered a smooth projective morphism $p:T\to S$ to a smooth variety $S$. It is proved, in particular, the following result. The total direct image $Rp_*(\Bbb Z/n\Bbb Z)$ of the constant \'etale sheaf $\Bbb Z/n\BZ$ is locally for Zarisky topology quasi-isomorphic to a bounded complex $\L$ on $S$ consisting of locally constant constructible \'etale $\Bbb Z/n\Bbb Z$-module sheaves.