### Variations on the Bloch-Ogus Theorem, by Ivan Panin and Kirill Zainoulline

In the present paper we discuss questions concerning
the arithmetic resolution for etale cohomology.
Namely, consider a smooth quasi-projective variety *X*
over a field *k* together with the local scheme
*U=Spec O*_{X,x} at a point *x*.
Let *Y* be a smooth proper scheme over *U*.
We prove there is the Gersten-type exact sequence for etale cohomology
with coefficients in a locally constant etale sheaf
*F* of *Z/nZ*-modules on *Y*
which has finite stalks and *(n,char(k))=1*.

Ivan Panin <panin@pdmi.ras.ru>

Kirill Zainoulline <kirill@pdmi.ras.ru>