# On Suslin homology with integral coefficients in characteristic zero (with an appendix by Bruno Kahn)

## TL;DR

This paper characterizes the structure of Suslin homology groups with integral coefficients over schemes in characteristic zero, revealing they decompose into divisible, torsion, and finitely generated parts, with implications for scheme morphisms.

## Contribution

It provides a detailed structural decomposition of Suslin homology groups in characteristic zero and extends previous results with simplified proofs and broader generalizations.

## Key findings

- Suslin homology groups decompose into divisible, torsion, and finitely generated components.
- Homomorphisms between these groups are classified by their induced scheme morphisms.
- The appendix offers simplified proofs and generalizations of the main results.

## Abstract

We show that the Suslin homology group with integral coefficients of a scheme $X$ separated of finite type over an algebraically closed field of characteristic 0 is a direct sum of a uniquely divisible group, finite copies of $\mathbb{Q}/\mathbb{Z}$, and a finitely generated group. We also study the possible type of homomorphisms between such groups induced by the morphisms of schemes. An appendix written by Bruno Kahn is included, which simplifies the proofs and generalizes the results.