A module structure and a vanishing theorem for cycles with modulus
Abstract
We show that the higher Chow groups with modulus of Binda-Kerz-Saito for a smooth quasi-projective scheme is a module over the Chow ring of . 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 -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.
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