The nisnevich-topology tag has no wiki summary.

**7**

votes

**0**answers

264 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

**0**answers

101 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 étale topology.
I know this has to be true since (Morel-Voevodsky: ...

**2**

votes

**0**answers

114 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

**0**answers

318 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

**1**answer

440 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

**0**answers

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

**1**answer

453 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

**0**answers

199 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

**1**answer

495 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 ...