Understand when the height pairing comes into the picture.
Schneider gives refs to three independent constructions of the height pairing: Beilinson, Bloch, and GS: Intersection sur les varieties d’Arakelov (C R Acad 299, 563-566 (1984) )
Beilinson’s original article
Scholl: Height.dvi for “motivic reinterpretation”
nLab page on Beilinson conjectures HEIGHT PAIRING