The p-adic Borel regulator injectivity conjecture

Let $k$ be a number field and let $p$ be a rational prime. For every odd dimension $2m-1\geq3$, consider the $p$-adic Borel regulator map

$$K_{2m-1}(k)\otimes_{\mathbb Z}{\mathbb Q}_p\longrightarrow\bigoplus_{v\mid p}k_v.$$

The $p$-adic Borel regulator injectivity conjecture. For every number field $k$, every rational prime $p$, and every odd dimension $2m-1\geq3$, this map is injective.

The conjecture is expected to hold in the stated generality and is the number-theoretic conjecture to which the paper reduces questions about profinite invariance of hyperbolic volume and arithmeticity.