2020/12/21 by Mainak Ghosh, Ghosh, Mainak, Amalendu Krishna +1
Mathematics · #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14C25 #Secondary 14F42
paper · pdf · doi:10.48550/arxiv.2012.11249
openalex publication_date 2020/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an extension of the Kato-Saito class field theory for smooth projective schemes over a finite field to schemes with singularities. As an application, we obtain Bloch's formula for the Chow groups of 0-cycles on such schemes. We identify the Chow group of 0-cycles on a normal projective scheme over an algebraically closed field to the Suslin homology of its regular locus. Our final result is a Roitman torsion theorem for smooth quasi-projective schemes over algebraically closed fields. This completes the missing p-torsion part in the torsion theorem of Spiess and Szamuely.