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, Rullling, 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.
Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus / F. Binda, J. Cao, W. Kai, R. Sugiyama. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 469(2017 Jan), pp. 437-463.
Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus
F. Binda
;
2017
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, Rullling, 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.File | Dimensione | Formato | |
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