I am looking for exact references for the comparison theorem for the étale fundamental group.
I mean the following result:



> 
> **Theorem** (Grothendieck). For a pointed algebraic variety $(X,x)$ over $\mathbb{C}$ there is a canonical isomorphism
>  between the étale fundamental group $\pi\_1^{\text{ét}}(X,x)$ and the profinite completion of the topological fundamental group
>  $\pi\_1^{\rm top}(X(\mathbb{C}),x)$.
> 
> 
> 


(I am interested in the case when $X$ is nonsingular.)


I could not find this assertion in SGA1 or in the book "Galois Groups and Fundamental Groups" by Tamás Szamuely. Please help!



Reference request: the comparison theorem for the étale fundamental group
This is in SGA1, Exposé XII, Section 5.


