Arithmetic 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 Soulé. 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.

31 Pages; Minor corrections were made, and two examples of arithmetic Chow groups with modulus were added