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Pullback and Weil transfer on Chow groups

Nikita Karpenko, Guangzhao Zhu

Abstract

In the paper ``Weil transfer of algebraic cycles'', published by the second author in Indagationes Mathematicae about 25 years ago, a Weil transfer map for Chow groups of smooth algebraic varieties has been constructed and its basic properties have been established. The proof of commutativity with the pullback homomorphisms given there used a variant of Moving Lemma suffering a lack of reference. Here we are providing an alternative proof based on a more contemporary construction of the pullback via a deformation to the normal cone.

Pullback and Weil transfer on Chow groups

Abstract

In the paper ``Weil transfer of algebraic cycles'', published by the second author in Indagationes Mathematicae about 25 years ago, a Weil transfer map for Chow groups of smooth algebraic varieties has been constructed and its basic properties have been established. The proof of commutativity with the pullback homomorphisms given there used a variant of Moving Lemma suffering a lack of reference. Here we are providing an alternative proof based on a more contemporary construction of the pullback via a deformation to the normal cone.

Paper Structure

This paper contains 2 theorems, 20 equations.

Key Result

Proposition 2

For any morphism $f\colon Y\to X$ of smooth $L$-varieties $Y$ and $X$, the square \begin{CD} \CH(Y) @<{f^*}<< \CH(X)\\ @V\cat{R}VV @VV\cat{R}V\\ \CH(R(Y)) @<R(f)^*<< \CH(R(X)) \end{CD}commutes.

Theorems & Definitions (5)

  • Example 1
  • Proposition 2: MR1809664
  • Lemma 4
  • proof
  • Remark 5