Regulators and derivatives of Vologodsky functions with respect to log(p)
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 \( (p) \). They can be differentiated with respect to this parameter and the result is related to the discrete component.
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