What Kind of Morphisms Induces Covering Maps over a Real Closed Field?
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929740224397312 |
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| author | Chen, Rizeng |
| author_facet | Chen, Rizeng |
| contents | In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite étale 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | What Kind of Morphisms Induces Covering Maps over a Real Closed Field? Chen, Rizeng Algebraic Geometry Symbolic Computation Primary 14P10, Secondary 14A10, 14Q30 In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite étale 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. |
| title | What Kind of Morphisms Induces Covering Maps over a Real Closed Field? |
| topic | Algebraic Geometry Symbolic Computation Primary 14P10, Secondary 14A10, 14Q30 |
| url | https://arxiv.org/abs/2502.05834 |