2024/11/27 by Semen Molokov, Vadim Vologodsky, Molokov, Semen +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2411.18274
openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that singular cohomology of the underlying space of Berkovich's analytification of a scheme X locally of finite type over a trivially-valued field k of characteristic 0 is isomorphic to cdh-cohomology with integer coefficients which is also isomorphic to the weight zero motivic cohomology H^*(X, ℤ). Using this isomorphism, we demonstrate the vanishing of RHom_ShNis(cork)(\underlineG,ℤ), where \underlineG denotes the Nisnevich sheaf with transfers associated with a commutative algebraic group G over k. For abelian k-varieties A and B, we prove that RHom_PShtr(\underlineA,\underlineB) is isomorphic to HomAbk(A,B).