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    • On flat pullbacks for Chow groups

      NITIN NITSURE

      Article Volume 132 Published: 8 September 2022 Article ID 0050

    • Fulltext

       

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      https://www.ias.ac.in/article/fulltext/pmsc/132/0050

    • Keywords

       

      Algebraic cycles; flat morphisms; rational equivalence; Chow groups.

    • Abstract

       

      It is a fundamental property of the Chow groups of algebraic schemes that they are contra-functorial with respect to flat morphisms between schemes. While thepullback homomorphism is easy to define at the level of algebraic cycles, the crucial step is to show that the pullback of cycles preserves rational equivalence, so that it descends to the Chow groups. The purpose of this note is to give a natural sheaf theoretic proof of the preservation of rational equivalence under flat pullback on cycles.

    • Author Affiliations

       

      NITIN NITSURE1

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

    • Dates

       
      Published
      8 September 2022
      Manuscript received
      24 January 2022
      Accepted
      16 April 2022
      Final version published online
      8 September 2022

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