  We study a local to global principle for certain higher zero-cycles over
global fields. We thereby verify a conjecture of Colliot-Th\'el\`ene for these
cycles. Our main tool are the Kato conjectures proved by Jannsen, Kerz and
Saito. Our approach also allows to reprove the ramified global class field
theory of Kato and Saito. Finally, we apply the Kato conjectures to study the
$p$-adic cycle class map over henselian discrete valuation rings of mixed
characteristic and to deduce finiteness theorems for arithmetic schemes in low
degree.
