For a nonsingular algebraic variety $X$ over the complex numbers, the functor $Y \mapsto Y^{an}$ which sends complex algebraic varieties to their complex analytic topology establishes an equivalence of categories between the corresponding étale sites $X_{et} \simeq X^{an}_{et}$.
James Milne, section 21 of Lectures on Étale Cohomology
Riemann’s existence theorem (pdf)
A related result in model theory:
We study elementary extensions of compact complex spaces and deduce that every complete type of dimension $1$ is internal to projective space. This amounts to a nonstandard version of the Riemann Existence Theorem, and answers a question posed by Anand Pillay.
Last revised on January 22, 2021 at 22:28:54. See the history of this page for a list of all contributions to it.