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arXiv · 2502.05834

What Kind of Morphisms Induces Covering Maps over a Real Closed Field?

Rizeng Chen
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Abstract

In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite \'etale after reduction. When $k$ is a real closed field, we prove that such a morphism induces a covering map on the rational points. We further give a triviality result different from Hardt's and a new interpretation of the construction of cylindrical algebraic decomposition as applications.

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Rizeng Chen. 2025-02-09. What Kind of Morphisms Induces Covering Maps over a Real Closed Field?. https://arxiv.org/abs/2502.05834

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