# Tagged Questions

**3**

votes

**2**answers

251 views

### homotopy exact sequence for the étale fundamental group

I have been trying to understand the homotopy exact sequence for the étale fundamental group which says
$ 1 \rightarrow \pi_1 \bar{X},\bar{x_0})\rightarrow \pi_1 (X,x_0)\rightarrow Gal(k)\rightarrow ...

**3**

votes

**1**answer

169 views

### Structure of fundamental groups arising from smooth projective morphisms

Let $f:X\to B$ be a smooth projective morphism of complex algebraic varieties.
If $f$ is of relative dimension zero, i.e., $f$ is a finite etale cover, then the image of the topological fundamental ...

**2**

votes

**2**answers

276 views

### About “de-Rham” and “l-adic” local systems - comparison

Hello,
Suppose that $k$ is an algebraically closed field of char. 0.
Let $X$ be a smooth connected variety over $k$.
Then I have the category $A$ of Regular Singular smooth $D$-modules on $X$ (i.e. ...