nLab
Riemann existence theorem

Contents

Contents

Statement

For a nonsingular algebraic variety XX over the complex numbers, the functor YY anY \mapsto Y^{an} which sends complex algebraic varieties to their complex analytic topology establishes an equivalence of categories between the corresponding étale sites X etX et anX_{et} \simeq X^{an}_{et}.

References

A related result in model theory:

  • Rahim Moosa ,_A nonstandard Riemann existence theorem_, Trans. Amer. Math. Soc. 356(5):1781–1797 (2004) doi

We study elementary extensions of compact complex spaces and deduce that every complete type of dimension 11 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 17:28:54. See the history of this page for a list of all contributions to it.