Arithmetic Cycles with Modulus

TL;DR

This paper introduces an arithmetic Chow group with modulus by incorporating analytic components and vanishing conditions, extending classical arithmetic Chow groups to include cycles with modulus.

Contribution

It defines a new arithmetic Chow group with modulus that combines algebraic and analytic data, generalizing classical constructions by Gillet and Soulé.

Findings

Established properties of the new arithmetic Chow group with modulus

Connected analytic components to cohomology vanishing conditions

Extended classical arithmetic Chow groups to cycles with modulus

Abstract

We add analytic components to algebraic cycles with modulus and define an arithmetic Chow group with modulus that resembles the classical arithmetic Chow groups by Gillet and Soul\'e. The analytic component is dictated by imposing a vanishing condition on the cohomology class of a cycle with modulus. We prove several natural properties of this group as a consequence.