Detecting motivic equivalences with motivic homology

2020/12/04 by David Hemminger, Hemminger, David
Mathematics · #14C15 #14F42 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2012.02351

openalex publication_date 2020/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a field, let R be a commutative ring, and assume the exponential characteristic of k is invertible in R. In this note, we prove that isomorphisms in Voevodsky's triangulated category of motives DM(k;R) are detected by motivic homology groups of base changes to all separable finitely generated field extensions of k. It then follows from previous conservativity results that these motivic homology groups detect isomorphisms between certain spaces in the pointed motivic homotopy category H(k)_*.

Related

• Intersecting the dimension filtration with the slice one for (relative) motivic categories
• Somekawa's K-groups and Voevodsky's Hom groups (preliminary version)
• Motives with modulus
• Hochschild homology of mod-p motivic cohomology over algebraically closed fields
• Splitting of abelian varieties in motivic stable homotopy category