Petersburg Department of Steklov Institute of Mathematics

PREPRINT 25/1998

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.