English

A module structure and a vanishing theorem for cycles with modulus

Algebraic Geometry 2016-05-12 v3 K-Theory and Homology

Abstract

We show that the higher Chow groups with modulus of Binda-Kerz-Saito for a smooth quasi-projective scheme XX is a module over the Chow ring of XX. From this, we deduce certain pull-backs, the projective bundle formula, and the blow-up formula for higher Chow groups with modulus. We prove vanishing of 00-cycles of higher Chow groups with modulus on various affine varieties of dimension at least two. This shows in particular that the multivariate analogue of Bloch-Esnault--R\"ulling computations of additive higher Chow groups of 0-cycles vanishes.

Keywords

Cite

@article{arxiv.1412.7396,
  title  = {A module structure and a vanishing theorem for cycles with modulus},
  author = {Amalendu Krishna and Jinhyun Park},
  journal= {arXiv preprint arXiv:1412.7396},
  year   = {2016}
}

Comments

v1: 32 pages; v2: 16 pages. Sections 2.4, 2.5, and Section 5 of v1 are removed. The removed part will be part of a different paper. Title was changed; v3: 18 pages. A version of this article was accepted to appear in MRL

R2 v1 2026-06-22T07:42:24.103Z