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7
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0answers
253 views

Nisnevich covers of algebraic spaces

Does every algebraic space have a Nisnevich cover by a scheme? (Assume that the algebraic space is quasi-separated, quasi-compact and over a scheme $S$.) Background: Every algebraic space has an ...
0
votes
0answers
99 views

Reference for Cech cohomology for Nisnevich topology

I need the theorems that prove that Nisnevich cohomology can be computed by the Cech complex similar to what happens in the ├ętale topology. I know this has to be true since (Morel-Voevodsky: ...
2
votes
0answers
111 views

Some 'weak proper and smooth base change' theorems for Nisnevich sheaves?

Among the most important tools for studying etale cohomology are the proper and smooth base change theorems. I suspect that these theorems are no longer true for Nisnevich cohomology (probably finite ...
4
votes
0answers
314 views

Cohomology of a sheaf with only one stalk

Let $X$ be a proper scheme over a henselian discrete valation ring. I have a Nisnevich sheaf $F$ of which has only one stalk at the generic point of $X$ (and all other stalks vanish). I believe that ...
4
votes
1answer
432 views

A Nisnevich cover which is not Zariski

The Nisnevich topology on $Sch$ is a Grothendieck topology strictly finer than the Zariski topology, and the etale topology is strictly finer than the Nisnevich topology. Colin McLarty asked me for ...
2
votes
0answers
125 views

Intersections of components of 'simple' ('local") Zariski coverings

I would like to study the ordered Cech cohomology with respect to a Zariski covering of a variety. I can pass to the limit with respect to refinements; the components of the 'limit covering' will be ...
6
votes
1answer
448 views

Basic properties of Nisnevich cohomology; $l'$-topology?

I would like to know more about Nisnevich cohomology (especially, on its properties that could be easily formulated). In particular, I would like to know which of the following statements are true, ...
2
votes
0answers
195 views

The restriction of the Gersten resolution (for etale cohomology) onto a closed subvariety.

There is a very important result of Bloch and Ogus: for any smooth variety $X$ and fixed $r\in \mathbb{Z}$, $r\ge 0$, $l$ is prime to the residue field characteristic, the Zariski sheafification of ...
5
votes
1answer
491 views

Nisnevich topology on non-(locally) Noetherian schemes

Background Lurie has in DAG XI a definition (given below) of a Nisnevich cover for arbitrary commutative rings, which reduces to the usual one for Noetherian rings. It boils down to being a etale ...