Geodesic
Variations on the Bloch-Ogus theorem
Documenta mathematica, Tome 8 (2003), pp. 51-67.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $R$ be a semi-local regular ring of geometric type over a field $k$. Let $\U=\spec R$ be the semi-local scheme. Consider a smooth proper morphism $p:Y \ra \U$. Let $Y_{k(u)}$ be the fiber over the generic point of a subvariety $u$ of $\U$. We prove that the Gersten-type complex for étale cohomology $$ 0 \ra \het^q(Y,C) \ra \het^q(Y_{k(\U)},C) \ra \coprod_{u\in \U^{(1)}} \het^{q-1}(Y_{k(u)},C(-1)) \ra\ldots $$ is exact, where $C$ is a locally constant sheaf with finite stalks of $\zz/n\zz$-modules on $Y_{et}$ and $n$ is an integer prime to $\chrt(k)$.
Classification : 14F20, 16E05
Keywords: étale cohomology, arithmetic resolution 
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     author = {Panin, Ivan and Zainoulline, Kirill},
     title = {Variations on the {Bloch-Ogus} theorem},
     journal = {Documenta mathematica},
     pages = {51--67},
     publisher = {mathdoc},
     volume = {8},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a16/}
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Panin, Ivan; Zainoulline, Kirill. Variations on the Bloch-Ogus theorem. Documenta mathematica, Tome 8 (2003), pp. 51-67. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a16/