# Arithmetic homology and an integral version of Katos conjecture

## TL;DR

This paper introduces an integral homology theory over finite fields, called arithmetic homology, and an integral version of Kato homology, proposing their properties and relationships with higher Chow groups.

## Contribution

It defines new integral homology theories over finite fields and explores their expected properties and connections to existing algebraic structures.

## Key findings

- Proposes an integral Borel-Moore homology theory over finite fields.
- Introduces an integral version of Kato homology.
- Suggests these groups are finitely generated and relate to higher Chow groups.

## Abstract

We define an integral Borel-Moore homology theory over finite fields, called arithmetic homology, and an integral version of Kato homology. Both types of groups are expected to be finitely generated, and sit in a long exact sequence with higher Chow groups of zero-cycles.