The ℓ-rank structure of a global function field
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Bibliographic record
Abstract
For any prime ℓ, it is possible to construct global function fields whose Jacobians have high ℓ-rank by moving to a sufficiently large constant field extension. This was investigated in some detail by Bauer et al. in [2]. The two main results of [2] are an upper bound on the size of the field of definition of the ℓ-torsion J [ℓ] of the Jacobian, and a lower bound on the increase in the base field size that guarantees a strict increase in ℓ-rank. Here, we provide improvements to both these results, and give examples which illustrate that our techniques have the potential to yield the correct ℓ-rank over any intermediate field of the field of definition of J [ℓ], including base fields that might be too large to be handled directly by computer algebra packages. 1
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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