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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2403.05453 |
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| _version_ | 1866909697628438528 |
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| author | Zhu, Hui June |
| author_facet | Zhu, Hui June |
| contents | Let A^d denote the coefficient space of all degree-d polynomials f in one variable for some d\ge 3. For any \bar{f} in A^d(\bar\F_p), a rank-\ell Artin-Schreier curve X_{\bar{f},\ell}: y^{p^\ell}-y= \bar{f} is called ordinary if its normalized Newton polygon achieves the infimum in A^d(\bar\F_p). Given \ell and a number field K, we show that there exists a Zariski dense open subset U in A^d, defined over Q, such that if f in U(K) then X_{(f\bmod \wp),\ell} is ordinary for all primes $\wp|p$ with deg(\wp) in \ell\Z and p large enough. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Variation of Elementary Abelian p-Extensions over $P^1$ Zhu, Hui June Number Theory Algebraic Geometry 11, 14 Let A^d denote the coefficient space of all degree-d polynomials f in one variable for some d\ge 3. For any \bar{f} in A^d(\bar\F_p), a rank-\ell Artin-Schreier curve X_{\bar{f},\ell}: y^{p^\ell}-y= \bar{f} is called ordinary if its normalized Newton polygon achieves the infimum in A^d(\bar\F_p). Given \ell and a number field K, we show that there exists a Zariski dense open subset U in A^d, defined over Q, such that if f in U(K) then X_{(f\bmod \wp),\ell} is ordinary for all primes $\wp|p$ with deg(\wp) in \ell\Z and p large enough. |
| title | Asymptotic Variation of Elementary Abelian p-Extensions over $P^1$ |
| topic | Number Theory Algebraic Geometry 11, 14 |
| url | https://arxiv.org/abs/2403.05453 |