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In mathematics, specifically complex analysis, Riemann's existence theorem says, in modern formulation, that the category of compact Riemann surfaces is equivalent to the category of complex algebraic curves.

= References

• Harbater, David. "Riemann’s existence theorem." The Legacy of Bernhard Riemann After 150 (2015)
• Ryan Patrick Catullo, Riemann Existence Theorem. A slide for the paper.
• SGA 1 and 4

Further reading

• https://mathoverflow.net/questions/80770/reference-request-riemanns-existence-theorem
• https://mathoverflow.net/questions/40791/finite-covers-of-complex-varieties-all-but-two-questions-answered
• https://ncatlab.org/nlab/show/Riemann+existence+theorem

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