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 OX,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>