@article{626f068915454eb2b514dff9c5133c38,
title = "Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus",
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{\"u}lling, 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.",
keywords = "Algebraic cycles, Chow groups, Motivic cohomology, Non-homotopy invariant motives, Reciprocity sheaves",
author = "F. Binda and J. Cao and W. Kai and R. Sugiyama",
note = "Funding Information: Large part of this work was carried out during the special semester in Motivic Homotopy Theory at the University of Duisburg-Essen (SS 2014). The authors wish to thank Marc Levine heartily for providing an excellent working environment and for the support via the Alexander von Humboldt foundation and the SFB Transregio 45 “Periods, moduli spaces and arithmetic of algebraic varieties”. The first author is supported by the DFG Schwerpunkt Programme 1786 “Homotopy theory and Algebraic Geometry”. The third author is supported by JSPS as a Research Fellow and through JSPS KAKENHI Grant ( 15J02264 ), and was supported by the Program for Leading Graduate Schools, MEXT , Japan during the work. The fourth author is supported by JSPS KAKENHI Grant ( 16K17579 ). We sincerely appreciate the referee's careful and valuable comments to an earlier draft of this paper, which helped us to significantly clarify and improve the exposition. Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",
year = "2017",
month = jan,
day = "1",
doi = "10.1016/j.jalgebra.2016.07.036",
language = "English",
volume = "469",
pages = "437--463",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}