On the interpolation property of Kupferer's Lubin-Tate regulator maps

Generalizing both [LZ14] and [ScV26, SaV24] we prove the interpolation property at Artin characters of Kupferer's regulator map [Ku20] over a fixed local field $L$ over $\mathbb{Q}_p$ for $p$ any prime. Since our methods cover the case $p=2,$ we in particular close a gap in the literature even for the (cyclotomic) 2-variable regulator map from [LZ14]. Moreover, we study big (dual) Bloch-Kato exponential maps for unramified towers and we use them to improve Colmez' reciprocity law in the Lubin-Tate setting from [SaV24]. Finally, we compare Kupferer's regulator map with the 2-variable regulator map of Loeffler-Zerbes when $L=\mathbb{Q}_p$.