English

A note on cubical Bloch--Levine cycle complexes

Algebraic Geometry 2026-07-01 v1

Abstract

We check that Levine's simplicial--cubical comparison argument for Bloch's cycle complexes also works over an arbitrary DVR. As a result, the sheaf of cubical Bloch cycle complexes computes motivic cohomology for smooth schemes over Dedekind bases.

Cite

@article{arxiv.2607.01540,
  title  = {A note on cubical Bloch--Levine cycle complexes},
  author = {Peter Xu},
  journal= {arXiv preprint arXiv:2607.01540},
  year   = {2026}
}