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keaton
keaton
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I'm reading Andrew Kresch's paper, Cycle groups in Artin Stacks.

The author defined Chow groups of Artin stacks by very technical way, instead of ordinary ways which he called 'naive chow group', quotient of free group generated by integral substacks by rational equivalence.

I don't understand why he used technical definition instead of ordinary one. What is the main failure arises when using 'naive chow groups'.group's?

I'm reading Andrew Kresch's paper, Cycle groups in Artin Stacks.

The author defined Chow groups of Artin stacks by very technical way, instead of ordinary ways which he called 'naive chow group', quotient of free group generated by integral substacks by rational equivalence.

I don't understand why he used technical definition instead of ordinary one. What is the main failure arises when using 'naive chow groups'.

I'm reading Andrew Kresch's paper, Cycle groups in Artin Stacks.

The author defined Chow groups of Artin stacks by very technical way, instead of ordinary ways which he called 'naive chow group', quotient of free group generated by integral substacks by rational equivalence.

I don't understand why he used technical definition instead of ordinary one. What is the main failure arises when using 'naive chow group's?

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keaton
keaton
  • 421
  • 2
  • 4

What is the main failure in using Naive Chow group in Artin Stack

I'm reading Andrew Kresch's paper, Cycle groups in Artin Stacks.

The author defined Chow groups of Artin stacks by very technical way, instead of ordinary ways which he called 'naive chow group', quotient of free group generated by integral substacks by rational equivalence.

I don't understand why he used technical definition instead of ordinary one. What is the main failure arises when using 'naive chow groups'.