A moving lemma for algebraic cycles with modulus and contravariance

Abstract

We prove a moving lemma which implies the contravariance of Bloch-Esnault's additive higher Chow group in smooth affine varieties and Binda-Saito's higher Chow group (taken in the Nisnevich topology) in smooth varieties equipped with effective Cartier divisors. The new ingredients in the moving method are parallel translation {\em with modulus} in the affine space that involves a new integer parameter, and Noether's normalization lemma over a Dedekind base.

arXiv commentv4: 39 pages. Rewritten for submission for publication

References in corpus (7)

• The homotopy coniveau tower
• Chow group of 0-cycles with modulus and higher dimensional class field theory
• Zero cycles with modulus and zero cycles on singular varieties
• Stable ${\mathbb{A}}^1$-connectivity over Dedekind schemes
• Multifractal Analysis of functions on Heisenberg and Carnot Groups
• Relative $K_0$ and relative cycle class map
• Moving Lemma for additive Chow groups and applications

Cited by in corpus (9)

• Zero cycles with modulus and zero cycles on singular varieties
• Notes on motivic infinite loop space theory
• Towards conservativity of ${\mathbb{G}}_m$-stabilization
• A moving lemma for relative $0$-cycles
• Nisnevich local Good compactifications
• Cube invariance of higher Chow groups with modulus
• On extension of the motivic cohomology beyond smooth schemes
• Gabber presentation lemma over noetherian domains
• Unramified logarithmic Hodge-Witt cohomology and ${\mathbb{P}}^1$-invariance