# Tagged Questions

**6**

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### Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?

Let $X$ be a variety over an algebraically closed field $k$. Denote by $\eta$ its generic point; it is the inverse limit of the open subvarieties $X_i$ of $X$. It is well known that the etale ...

**6**

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**0**answers

96 views

### References for Gauss Composition using Galois Cohomology

Note: I have already posted this on stackexchange, but have not yet gotten a response.
What are some good references for the Gauss composition law on binary quadratic forms in terms of Galois ...

**1**

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**1**answer

247 views

### Cohomology after completion

I've been scouring google and asking friend about something I was certain must be absolutely the easiest thing to people who do homological algebra, and none seem to know the answer to this, so if ...

**3**

votes

**1**answer

72 views

### Set of isomorphisms of Pfister forms corresponding to first cohomology of algebraic group

Assume $k_0$ is a field with char($k_0$) not $2$. Let us define functors from $\rm Field_{/k_0}\to \rm Sets$ as $\rm Pfister_n(k):=\{\text{isomorphism classes of n-fold Pfister forms over k}\}$;
...

**2**

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**1**answer

130 views

### the sixth morphism in the long exact sequence associated to the Hochschild-Serre spectral sequence

The long exact sequence associated to the Hochschild-Serre spectral sequence for extension of groups $1 \to H \to G \to G/H \to 1$ is
$$
\begin{array}[t]{lll}
1 \to & H^1(G/H, A^{G/H}) ...

**0**

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**0**answers

217 views

### Ordered Cech(-like) complexes that compute etale cohomology (of fields!)

It is well known (cf. Equivalence of ordered and unordered cech cohomology. ) that for 'usual' topologies one can compute the cohomology of sheaves either using unordered Cech complexes or ordered ...

**5**

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**1**answer

767 views

### Galois groups via cohomology

I would like to know about references for the following result (point 3):
Let $K/k$ be a normal extension (I am interested in number fields, but everything should work in fields of characteristic ...