Reciprocity sheaves and logarithmic motives

2021/07/01 by Saito, Shuji
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.00381

Abstract

We connect two developments aiming at extending Voevodsky's theory of motives over a field in such a way to encompass non-A¹-invariant phenomina. One is theory of reciprocity sheaves introduced by Kahn-Saito-Yamazaki. Another is theory of the triangulated category logDM^eff of logarithmic motives launched by Binda, Park and Østvær. We prove that the Nisnevich cohomology of reciprocity sheaves is representable in logDM^eff.

Related

• Triangulated categories of logarithmic motives over a field
• Some computations in the heart of the homotopy t-structure on logarithmic motives
• Lectures on the cohomology of reciprocity sheaves
• Logarithmic motives with compact support
• On the triangulated category of framed motives DFr_-^eff(k)