K-theory and 0-cycles on schemes
Rahul Gupta, Amalendu Krishna
TL;DR
This paper proves Bloch's formula for 0-cycles on certain schemes over algebraically closed fields, extending its validity and deriving applications like 0-cycles with modulus.
Contribution
It establishes Bloch's formula for affine schemes and regular codimension-one schemes, and applies it to 0-cycles with modulus.
Findings
Bloch's formula proven for affine schemes over algebraically closed fields.
Extended Bloch's formula to projective regular schemes in codimension one.
Derived applications including Bloch's formula for 0-cycles with modulus.
Abstract
We prove Bloch's formula for 0-cycles on affine schemes over algebraically closed fields. We prove this formula also for projective schemes over algebraically closed fields which are regular in codimension one. Several applications, including Bloch's formula for 0-cycles with modulus, are derived.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology