  Let $p$ be a prime number, and let $k$ be an algebraically closed field of
characteristic $p$. We show that the tame fundamental group of a smooth affine
curve over $k$ is a projective profinite group. We prove that the fundamental
group of a smooth projective variety over $k$ is finitely presented. More
generally we prove that the tame fundamental group of a smooth quasi-projective
variety over $k$ which admits a good compactification is finitely presented.
  v2: references added. Thank you to all for the friendly and fruitful
comments.
