A moving lemma for cycles with very ample modulus

TL;DR

This paper establishes a moving lemma for higher Chow groups with very ample modulus on projective schemes, enabling new functoriality results and vanishing theorems for specific cases.

Contribution

It introduces the first moving lemma for cycles with very ample modulus, expanding the scope beyond additive higher Chow groups.

Findings

Proves a moving lemma for higher Chow groups with very ample modulus

Demonstrates contravariant functoriality of these Chow groups

Shows vanishing of higher Chow groups for line bundles with zero section as modulus

Abstract

We prove a moving lemma for higher Chow groups with modulus, in the sense of Binda-Kerz-Saito, of projective schemes when the modulus is given by a very ample divisor. This provides one of the first cases of moving lemmas for cycles with modulus, not covered by the additive higher Chow groups. We apply this to prove a contravariant functoriality of higher Chow groups with modulus. We use our moving techniques to show that the higher Chow groups of a line bundle over a scheme, with the 0-section as the modulus, vanishes.