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

2015/03/07 by Federico Binda, Binda, Federico, Jin Cao +5
Mathematics · #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1503.02161

openalex publication_date 2015/03/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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, Rülling, 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.

Related

• Torsion zero cycles with modulus on affine varieties
• Torsion in the 0-cycle group with modulus
• Zero-cycle groups on algebraic varieties
• Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory
• Suslin homology via cycles with modulus and applications