Geometry-of-numbers methods over global fields II: Coregular representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914486489710592 |
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| author | Bhargava, Manjul Shankar, Arul Wang, Xiaoheng |
| author_facet | Bhargava, Manjul Shankar, Arul Wang, Xiaoheng |
| contents | We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ranks and determine average Selmer group sizes of elliptic curves and Jacobians of hyperelliptic curves over any base global field $F$ of characteristic not $2$, $3$ or $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry-of-numbers methods over global fields II: Coregular representations Bhargava, Manjul Shankar, Arul Wang, Xiaoheng Number Theory 11R29, 11R45 We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ranks and determine average Selmer group sizes of elliptic curves and Jacobians of hyperelliptic curves over any base global field $F$ of characteristic not $2$, $3$ or $5$. |
| title | Geometry-of-numbers methods over global fields II: Coregular representations |
| topic | Number Theory 11R29, 11R45 |
| url | https://arxiv.org/abs/2604.16978 |