A decomposition theorem for 0-cycles and applications

TL;DR

This paper establishes a decomposition theorem for 0-cycle cohomological Chow groups on doubles of schemes, generalizing prior results and enabling new applications like a moving lemma and an analogue of Bloch's formula for singular surfaces.

Contribution

It introduces a new decomposition theorem for 0-cycle Chow groups on doubles of schemes, extending previous work and providing tools for studying 0-cycles with modulus on singular surfaces.

Findings

Proved a decomposition theorem for cohomological Chow groups of 0-cycles.

Established a moving lemma for Chow groups with modulus.

Extended Bloch's formula to 0-cycles with modulus on singular surfaces.

Abstract

We prove a decomposition theorem for the cohomological Chow group of 0-cycles on the double of a quasi-projective $R_1$-scheme over a field along a closed subscheme, in terms of the Chow groups, with and without modulus, of the scheme. This yields a significant generalization of the decomposition theorem of Binda-Krishna. As applications, we prove a moving lemma for Chow groups with modulus and an analogue of Bloch's formula for 0-cycles with modulus on singular surfaces. The latter extends a previous result of Binda-Krishna-Saito.