English

A local to global principle for higher zero-cycles

Algebraic Geometry 2019-06-12 v2

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 pp-adic cycle class map over henselian discrete valuation rings of mixed characteristic and to deduce finiteness theorems for arithmetic schemes in low degree.

Keywords

Cite

@article{arxiv.1903.05184,
  title  = {A local to global principle for higher zero-cycles},
  author = {Johann Haas and Morten Lüders},
  journal= {arXiv preprint arXiv:1903.05184},
  year   = {2019}
}

Comments

19 pages, more references, more general main theorem, corrections

R2 v1 2026-06-23T08:06:19.153Z