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

F. Binda, J. Cao, W. Kai, R. Sugiyama

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)437-463
Number of pages27
JournalJournal of Algebra
Publication statusPublished - 2017 Jan 1
Externally publishedYes


  • Algebraic cycles
  • Chow groups
  • Motivic cohomology
  • Non-homotopy invariant motives
  • Reciprocity sheaves

ASJC Scopus subject areas

  • Algebra and Number Theory


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