Regulators and derivatives of Vologodsky functions with respect to log(p)

Amnon Besser

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arXiv · 2502.16738

Regulators and derivatives of Vologodsky functions with respect to log(p)

Amnon Besser

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Abstract

We describe several instances of the following phenomenon: In bad reduction situations the $ p $-adic regulator has a continuous and a discrete component. The continuous component is computed using Vologodsky integrals. These depend on a choice of the branch of the $ p $-adic logarithm, determined by $ \log (p) $. They can be differentiated with respect to this parameter and the result is related to the discrete component.

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Amnon Besser. 2025-02-23. Regulators and derivatives of Vologodsky functions with respect to log(p). https://arxiv.org/abs/2502.16738

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