The etale-cohomology tag has no wiki summary.

**5**

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**2**answers

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### loaclly constant constructible sheaves and finite etale coverings

Maybe it is well known to experts or maybe it is just a stupid idea, but I will ask any way.
We know that if $X$ is a topological space, then there is an equivalence of categories between the ...

**9**

votes

**0**answers

209 views

### L-Functions of Varieties, Zeta Functions of Their Models

Let $k$ denote a number field, with algebraic closure $\bar{k}$. Take a smooth, projective variety $X$ over $k$. If $\mathfrak{p}$ is a prime of $k$, and $l$ is a rational prime different to the ...

**4**

votes

**2**answers

447 views

### Twisted forms and $\check{H}^1$

I am reading Milne's Étale cohomology, III.4.
A twisted form of an object $Y$ (a scheme, a sheaf of modules, of algebras...) over a scheme $X$ is an object $Y'$ such that there exists a covering in ...

**3**

votes

**1**answer

706 views

### Galois cohomology groups given by étale cohomology

What are cases when Galois cohomology groups are given by étale cohomology?
Example: $S = Spec(K)$ the spectrum of a field, $F \in Sh(K)$, then $H^p(K, F) = H^p(G_K, F_{\bar{K}})$.
What if $G = ...

**5**

votes

**1**answer

438 views

### Semisimplicity of Frobenius operation on etale cohomology?

Let $X_0$ be a variety defined over a finite field of characteristic $p \neq l$.
Is it true, that the action of the frobenius on the l-adic cohomology $H_l^*(X)$ is semisimple (say for smooth $X_0$)? ...

**2**

votes

**1**answer

249 views

### commutative diagram with Yoneda pairing, Weil pairing and edge morphism

Why does the following diagram commute?$\require{AMScd}$
\begin{CD}
H^0(X,\mathscr{A}) \times \mathrm{Ext}^2_X(\mathscr{A},\mu_{\ell^n}) @>>> H^2(X,\mu_{\ell^n}) \\ @VVV @| \\
...