# motivic integration and jacobian ideal

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,

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