On rational connectedness and parametrization of finite Galois extensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929725010608128 |
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| author | Krashen, Daniel Neftin, Danny |
| author_facet | Krashen, Daniel Neftin, Danny |
| contents | Given two $G$-Galois extensions of $\mathbb Q$, is there an extension of $\mathbb Q(t)$ that specializes to both? The equivalence relation on $G$-Galois extension of $\mathbb Q$, induced by the above question, is called $R$-equivalence. The number of $R$-equivlance classes indicates how many rational spaces are required in order to parametrize all $G$-Galois extensions of $\mathbb Q$. We determine the $R$-equivalence classes for basic families of groups $G$, and consequently obtain parametrizations of the $G$-Galois extensions of $\mathbb Q$ in the absence of a generic extension for $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On rational connectedness and parametrization of finite Galois extensions Krashen, Daniel Neftin, Danny Number Theory Algebraic Geometry Given two $G$-Galois extensions of $\mathbb Q$, is there an extension of $\mathbb Q(t)$ that specializes to both? The equivalence relation on $G$-Galois extension of $\mathbb Q$, induced by the above question, is called $R$-equivalence. The number of $R$-equivlance classes indicates how many rational spaces are required in order to parametrize all $G$-Galois extensions of $\mathbb Q$. We determine the $R$-equivalence classes for basic families of groups $G$, and consequently obtain parametrizations of the $G$-Galois extensions of $\mathbb Q$ in the absence of a generic extension for $G$. |
| title | On rational connectedness and parametrization of finite Galois extensions |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2502.15674 |