2025/09/19 by Ivan Hernandez, Hernandez, Ivan, Pablo Pelaez +1
Engineering · Mathematics · #14C15 #14C25 #19E15 #Advanced Mathematical Theories #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2509.15920
openalex publication_date 2025/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth projective variety of dimension d over an algebraically closed field k. The main goal of this paper is to study, in the context of Voevodsky's triangulated category of motives DMk, the group CHnalg(X) of codimension n algebraic cycles of X, algebraically equivalent to zero, modulo rational equivalence, 1≤ n ≤ d. Namely, for any regular homomorphism ψ (in the sense of Samuel) defined on CHnalg(X), we construct Mnψ(X)∈ DMk, which is a reasonable approximation, with respect to the slice filtration in DMk, of the motive of X, M(X); and a map zψ: Mnψ(X)→ M(X) in DMk, which computes the kernel of ψ. We construct as well a map, zabn: Mnab(X) → M(X) having analogue properties but which instead computes the subgroup CHnab(X)⊆ CHnalg(X) of algebraic cycles abelian equivalent to zero (in the sense of Samuel).