Riemann surfaces and the Galois correspondence

Junyang Yu

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arXiv · 1708.06282

Riemann surfaces and the Galois correspondence

Junyang Yu

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Abstract

In this paper we introduce a space with some additional topologies using filter bases and renew the definition of Riemann surfaces of algebraic functions. We then present a Galois correspondence between these Riemann surfaces and their deck transformation groups. We also extend the monodromy theorem to the case that the global analytic function possesses singularities, which can be non-isolated.

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Junyang Yu. 2017-08-21. Riemann surfaces and the Galois correspondence. https://arxiv.org/abs/1708.06282

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