2018/12/31 by Fangzhou Jin, Enlin Yang · 9 citations
Mathematics · #Additive function #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Class (philosophy) #Combinatorics #Euler characteristic #Euler's formula #Homotopy #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical analysis #Mathematics #Morphism #Pairing #Pure mathematics #Transversality #math.AG #math.KT #msc:14F42 #msc:19E15
paper · pdf · doi:10.1016/j.aim.2020.107446
published in Advances in Mathematics 376, 107446 (Elsevier BV) · 58 pages; updated two references
arxiv created 2019/03/29 · openalex publication_date 2020/10/16 · arxiv updated 2021/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove several Künneth formulas in motivic homotopy categories and deduce a Verdier pairing in these categories following SGA5, which leads to the characteristic class of a constructible motive, an invariant closely related to the Euler-Poincaré characteristic. We prove an additivity property of the Verdier pairing using the language of derivators, following the approach of May and Groth-Ponto-Shulman; using such a result we show that in the presence of a Chow weight structure, the characteristic class for all constructible motives is uniquely characterized by proper covariance, additivity along distinguished triangles, refined Gysin morphisms and Euler classes. In the relative setting, we prove the relative Künneth formulas under some transversality conditions, and define the relative characteristic class.