Exponents of Jacobians and relative class groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912073786589184 |
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| author | Kadets, Borys Keliher, Daniel |
| author_facet | Kadets, Borys Keliher, Daniel |
| contents | We prove a lower bound for the exponent of the relative class group $\mathrm{Pic}^0 X_1/ϕ^* \mathrm{Pic}^0 X_2$ for a covering of curves $X_1 \to X_2$ over a finite field $\mathbb{F}_q$. The results improve on the existing best bounds (due to Stichtenoth) in the case $X_2=\mathbb{P}^1$, when the relative class group equals the class group of the function field $\mathbb{F}_q(X_1)$, and are completely new for the genuinely relative situation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponents of Jacobians and relative class groups Kadets, Borys Keliher, Daniel Number Theory Algebraic Geometry 11R58, 11R29, 14H40 We prove a lower bound for the exponent of the relative class group $\mathrm{Pic}^0 X_1/ϕ^* \mathrm{Pic}^0 X_2$ for a covering of curves $X_1 \to X_2$ over a finite field $\mathbb{F}_q$. The results improve on the existing best bounds (due to Stichtenoth) in the case $X_2=\mathbb{P}^1$, when the relative class group equals the class group of the function field $\mathbb{F}_q(X_1)$, and are completely new for the genuinely relative situation. |
| title | Exponents of Jacobians and relative class groups |
| topic | Number Theory Algebraic Geometry 11R58, 11R29, 14H40 |
| url | https://arxiv.org/abs/2410.11962 |