0
votes
3answers
223 views

question about the induced homomorphism of etale fundamental groups

Background/Setup For any connected scheme $S$, let $\text{FEt}_S$ denote the category of finite etale $S$-schemes. Let $f : X\rightarrow Y$ be a morphism of connected schemes, then for any finite ...
3
votes
2answers
290 views

homotopy exact sequence for the étale fundamental group

I have been trying to understand the homotopy exact sequence for the ├ętale 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
1answer
179 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
2answers
287 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. ...