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arXiv · 2504.03430

A P-adic class formula for Anderson t-modules

Alexis Lucas
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Abstract

Let $P$ be a monic prime of $\mathbb F_q[\theta]$, we define the $P$-adic $L$-series associated with Anderson $t$-modules and prove a $P$-adic class formula \`a 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 \`a la Pellarin. Finally, we give some applications to Drinfeld modules defined over $\mathbb F_q[\theta]$ itself.

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Alexis Lucas. 2025-04-04. A P-adic class formula for Anderson t-modules. https://arxiv.org/abs/2504.03430

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