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A P-adic class formula for Anderson t-modules (2504.03430v2)

Published 4 Apr 2025 in math.NT

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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