The comparison of the 0-th Suslin homology and Chow groups of 0-cycles with modulus

2024/12/05 by Nakamura, Teppei
Mathematics · #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 14C25 #Secondary 14F42

paper · pdf · doi:10.48550/arxiv.2412.03891

openalex publication_date 2024/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, for a K₀-regular projective normal surface X over a perfect field k of positive characteristic and a reduced effective Cartier divisor D\hookrightarrow X, the Chow group of zero cycles on X with modulus D coincides with the 0-th Suslin homology of X∖ D. Moreover, we show that this isomorphism also holds for a projective smooth scheme of any dimension with a reduced effective Cartier divisor.

Related

• Suslin homology via cycles with modulus and applications
• Zero-cycle groups on algebraic varieties
• On 0-cycles with modulus
• Zero-cycles on normal varieties
• Cycle class maps for Chow groups of zero-cycles with modulus