Arithmetic Cycles with Modulus

2025/01/06 by Goswami, Souvik, Gupta, Rahul
#14C22 #14C25 #14G40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.03408

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.

Related

• Idele class groups with modulus
• A module structure and a vanishing theorem for cycles with modulus
• A moving lemma for cycles with very ample modulus
• Cohomological arithmetic Chow rings
• Cycle class maps for Chow groups of zero-cycles with modulus