• On flat pullbacks for Chow groups

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    • 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



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

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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