On additive higher Chow groups of affine schemes

2015/04/30 by Amalendu Krishna, Krishna, Amalendu, Jinhyun Park +1
Mathematics · Physics and Astronomy · #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Primary 14C25 #Secondary 13F35 #math.AG #math.KT #msc:13F35 #msc:14C25 #msc:19E15

paper · pdf · doi:10.48550/arxiv.1504.08185

v1: 35 pages. Preliminary version. Comments welcome. Some sections deleted from arXiv:1412.7396 merged. / v2: 34 pages. Revised. / v3: 32 pages. Revised, compactified. /v4: W. Kai's 1507.07619 reflected. /v5: 36 pages. A variation of this version was accepted to appear in Documenta Mathematica. The present version is NOT the final accepted version, not to cause copyright issues

openalex publication_date 2015/04/30 · arxiv created 2015/12/24 · arxiv updated 2015/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the multivariate additive higher Chow groups of a smooth affine k-scheme \Spec (R) essentially of finite type over a perfect field k of characteristic \not = 2 form a differential graded module over the big de Rham-Witt complex \W_mΩ^\bullet_R. In the univariate case, we show that additive higher Chow groups of \Spec (R) form a Witt-complex over R. We use these structures to prove an étale descent for multivariate additive higher Chow groups.

Citations

• A module structure and a vanishing theorem for cycles with modulus

Related

• Additive Chow groups of schemes
• Additive Chow groups with higher modulus and the generalized de Rham-Witt complex
• de Rham-Witt sheaves via algebraic cycles
• An additive version of higher Chow groups
• On two higher Chow groups of schemes over a finite field