Ramification of Tate modules for rank $2$ Drinfeld modules
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909315349086208 |
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| author | Asayama, Takuya Huang, Maozhou |
| author_facet | Asayama, Takuya Huang, Maozhou |
| contents | In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modules are defined as analogues of those for elliptic curves. A calculation of these conductors allows us to show an analogue of Szpiro's conjecture under a certain limited situation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13275 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ramification of Tate modules for rank $2$ Drinfeld modules Asayama, Takuya Huang, Maozhou Number Theory 11G09, 11S15, 11S20, 11F80 In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modules are defined as analogues of those for elliptic curves. A calculation of these conductors allows us to show an analogue of Szpiro's conjecture under a certain limited situation. |
| title | Ramification of Tate modules for rank $2$ Drinfeld modules |
| topic | Number Theory 11G09, 11S15, 11S20, 11F80 |
| url | https://arxiv.org/abs/2204.13275 |