# PREPRINT 25/1998

I. PANIN and A. SMIRNOV

## ON A THEOREM OF GROTHENDIECK

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.



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