Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus

TL;DR

This paper investigates the torsion and divisibility properties of Chow groups of 0-cycles with modulus, connecting classical notions of modulus with modern sheaf theory and algebraic cycles.

Contribution

It establishes torsion and divisibility results for non-homotopy invariant parts of Chow groups with modulus, linking them to sheaf-theoretic generalizations.

Findings

Proves torsion properties of Chow groups with modulus.

Shows divisibility properties of these groups.

Extends results to sheaves in the context of algebraic cycles.

Abstract

The notion of modulus is a striking feature of Rosenlicht-Serre's theory of generalized Jacobian varieties of curves. It was carried over to algebraic cycles on general varieties by Bloch-Esnault, Park, R\"ulling, Krishna-Levine. Recently, Kerz-Saito introduced a notion of Chow group of $0$-cycles with modulus in connection with geometric class field theory with wild ramification for varieties over finite fields. We study the non-homotopy invariant part of the Chow group of $0$-cycles with modulus and show their torsion and divisibility properties. Modulus is being brought to sheaf theory by Kahn-Saito-Yamazaki in their attempt to construct a generalization of Voevodsky-Suslin-Friedlander's theory of homotopy invariant presheaves with transfers. We prove parallel results about torsion and divisibility properties for them.