# Transformation rule for motivic integration: divisors or divisors classes?

In the Kontsevich's 'change of variables for motivic integral' rule does one consider any possible choices for the corresponding canonical divisors, or is it necessary to fix certain representatives in these canonical classes?

If the first answer is the right one, how does one prove the independence from the choice of representatives? If the second answer is the right one, how does one control these representatives?

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