Murthy's conjecture on 0-cycles

TL;DR

This paper proves that the Levine-Weibel Chow group of 0-cycles for certain affine algebras is torsion-free, leading to a solution of Murthy's conjecture in classical K-theory.

Contribution

It establishes the torsion-freeness of the Levine-Weibel Chow group for reduced affine algebras of dimension at least 2, solving Murthy's longstanding conjecture.

Findings

Levine-Weibel Chow group is torsion-free for the specified algebras.

The result confirms Murthy's conjecture in classical K-theory.

Provides new insights into the structure of 0-cycles in algebraic geometry.

Abstract

We show that the Levine-Weibel Chow group of 0-cycles $\CH^d(A)$ of a reduced affine algebra $A$ of dimension $d \ge 2$ over an algebraically closed field is torsion-free. Among several applications, it implies an affirmative solution to an old conjecture of Murthy in classical $K$-theory..