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

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• 作者：F. Binda^a ; ^{federico.binda@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; J. Cao^a ; ^{jin.cao@stud.uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; W. Kai^b ; ^{kaiw@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; R. Sugiyama^c ; ^{rin@mail.dendai.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 14C25 ; secondary ; 19E15 ; 14F42
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：469
• 期：Complete
• 页码：437-463
• 全文大小：532 K

文摘

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.