# A local to global principle for higher zero-cycles

## TL;DR

This paper establishes a local to global principle for higher zero-cycles over global fields, confirming a conjecture of Colliot-Thélène using the Kato conjectures and their implications for class field theory and arithmetic schemes.

## Contribution

It verifies Colliot-Thélène's conjecture for higher zero-cycles and applies Kato conjectures to various problems in arithmetic geometry.

## Key findings

- Verification of Colliot-Thélène's conjecture for certain zero-cycles
- Reproof of ramified global class field theory of Kato and Saito
- Finiteness results for arithmetic schemes in low degree

## Abstract

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.