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Murthy’s conjecture on 0-cycles

  • Amalendu KrishnaEmail author
Article
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Abstract

We show that the Levine–Weibel Chow group of 0-cycles \(\mathrm{CH}^d(A)\) 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.

Mathematics Subject Classification

Primary 14C25 Secondary 14C35 19E08 14R99 

Notes

Acknowledgements

The author would like to thank M. K. Das for help in locating a reference for the relation between the Euler and weak Euler class groups. He would like to thank Marc Levine for encouragement and, S. M. Bhatwadekar and Chuck Weibel for useful comments on this paper. The author is grateful to the referee for many comments and suggestions which greatly improved the exposition of this paper.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

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