# Contents

## Idea

The analytic topology on an complex analytic space is the one given by covering the space by affine opens equipped with the standard topology induced from that of the complex numbers $\mathbb{C}^n$.

## Properties

### Comparison theorem

Chow's theorem states that a projective complex analytic variety, hence a closed analytic subspace of a complex projective space, is also an algebraic variety over the complex numbers. In general this is not true.

The comparison theorem (étale cohomology) relates the étale cohomology of a complex variety with the ordinary cohomology of its complex analytic topological space.

For more along such lines see at GAGA.

## References

Last revised on October 24, 2014 at 18:41:14. See the history of this page for a list of all contributions to it.