Diophantine stability and second order terms
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913506612215808 |
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| author | Pagano, Carlo Sofos, Efthymios |
| author_facet | Pagano, Carlo Sofos, Efthymios |
| contents | We establish a Galois-theoretic trichotomy governing Diophantine stability for genus $0$ curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine stable with probability $1$. Our asymptotic formula for the second order term exhibits strong bias towards instability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diophantine stability and second order terms Pagano, Carlo Sofos, Efthymios Number Theory 11E12, 11N36, 14G05 We establish a Galois-theoretic trichotomy governing Diophantine stability for genus $0$ curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine stable with probability $1$. Our asymptotic formula for the second order term exhibits strong bias towards instability. |
| title | Diophantine stability and second order terms |
| topic | Number Theory 11E12, 11N36, 14G05 |
| url | https://arxiv.org/abs/2409.12144 |