Reciprocity sheaves and logarithmic motives. Issue 2 (13th February 2023)

• Record Type: Journal Article
• Authors: Saito, Shuji
• Is Part Of: Compositio mathematica. Volume 159:Issue 2(2023)
• Page Start: 355
• Page End: 379
• Publication Date: 2023-02-13
• Subjects: motives -- reciprocity sheaves -- logarithmic geometry; 14F42 -- 14F06 -- 14C25 -- 14A21; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X22007862
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We connect two developments that aim to extend Voevodsky's theory of motives over a field in such a way as to encompass non- $\mathbf {A}^1$ -invariant phenomena. One is theory of reciprocity sheaves introduced by Kahn, Saito and Yamazaki. The other is theory of the triangulated category $\operatorname {\mathbf {logDM}}^{{\operatorname {eff}}}$ of logarithmic motives launched by Binda, Park and Østvær. We prove that the Nisnevich cohomology of reciprocity sheaves is representable in $\operatorname {\mathbf {logDM}}^{{\operatorname {eff}}}$ .