Effective rigid analytic trivializations for Drinfeld modules
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866918116846469120 |
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| author | Khaochim, Chalinee Papanikolas, Matthew A. |
| author_facet | Khaochim, Chalinee Papanikolas, Matthew A. |
| contents | We develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson generating functions. One advantage is that these infinite products can be obtained from only a finite amount of initial calculation, and consequently we obtain new formulas for periods and quasi-periods, similar to the product expansion of the Carlitz period. We further link to results of Gekeler and Maurischat on the $\infty$-adic field generated by the period lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_02670 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Effective rigid analytic trivializations for Drinfeld modules Khaochim, Chalinee Papanikolas, Matthew A. Number Theory 11G09 (Primary), 12H10, 33E50 (Secondary) We develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson generating functions. One advantage is that these infinite products can be obtained from only a finite amount of initial calculation, and consequently we obtain new formulas for periods and quasi-periods, similar to the product expansion of the Carlitz period. We further link to results of Gekeler and Maurischat on the $\infty$-adic field generated by the period lattice. |
| title | Effective rigid analytic trivializations for Drinfeld modules |
| topic | Number Theory 11G09 (Primary), 12H10, 33E50 (Secondary) |
| url | https://arxiv.org/abs/2104.02670 |