A P-adic class formula for Anderson t-modules
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909568090505216 |
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| author | Lucas, Alexis |
| author_facet | Lucas, Alexis |
| contents | Let $P$ be a monic prime of $\mathbb F_q[θ]$, we define the $P$-adic $L$-series associated with Anderson $t$-modules and prove a $P$-adic class formula à la Taelman linking a $P$-adic regulator, the class module and a local factor at $P$. Next, we extend this result to the multi-variable setting à la Pellarin. Finally, we give some applications to Drinfeld modules defined over $\mathbb F_q[θ]$ itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A P-adic class formula for Anderson t-modules Lucas, Alexis Number Theory 11G09, 11M38, 11R58 Let $P$ be a monic prime of $\mathbb F_q[θ]$, we define the $P$-adic $L$-series associated with Anderson $t$-modules and prove a $P$-adic class formula à la Taelman linking a $P$-adic regulator, the class module and a local factor at $P$. Next, we extend this result to the multi-variable setting à la Pellarin. Finally, we give some applications to Drinfeld modules defined over $\mathbb F_q[θ]$ itself. |
| title | A P-adic class formula for Anderson t-modules |
| topic | Number Theory 11G09, 11M38, 11R58 |
| url | https://arxiv.org/abs/2504.03430 |