2018/08/31 by Marc Levine, Arpon Raksit · 22 citations
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Base (topology) #Cohomology #Euler characteristic #Homotopy #Homotopy and Cohomology in Algebraic Topology #Motivic cohomology #math.AG #math.AT #msc:14F42 #msc:55N20 #msc:55N35
paper · pdf · doi:10.2140/ant.2020.14.1801
published in Algebra & Number Theory 14(7), 1801-1851 (Mathematical Sciences Publishers) · Final version-to appear in Algebra & Number Theory
openalex created_date 2018/08/31 · arxiv created 2020/02/26 · openalex publication_date 2020/08/18 · arxiv updated 2020/08/26 · openalex updated_date 2026/08/05
The apparatus of motivic stable homotopy theory provides a notion of Euler characteristic for smooth projective varieties, valued in the Grothendieck–Witt ring of the base field. Previous work of the first author and recent work of Déglise, Jin and Khan established a motivic Gauss–Bonnet formula relating this Euler characteristic to pushforwards of Euler classes in motivic cohomology theories. We apply this formula to [math] -oriented motivic cohomology theories to obtain explicit characterizations of this Euler characteristic. The main new input is a uniqueness result for pushforward maps in [math] -oriented theories, identifying these maps concretely in examples of interest.