When we consider the change of variables in motivic integration, we have a birational map $f:Y\rightarrow X$ with Y smooth and we have to consider two invariants the order of the Jacobian ideal of $X$ and the one related to the map,

http://arxiv.org/pdf/math/0612862.pdf Thm 6.2

My question is as we have to lift sections on singular spaces, why the jacobian ideal is sufficient instead of the Elkik ideal and how they differ?

  • What is the Elkik ideal? – Takehiko Yasuda Oct 18 '14 at 12:17
  • look at Elkik paper on approximations of solutions... – prochet Oct 19 '14 at 5:45

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