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added pointer to this new textbook
(Somebody should write a paragraph into this entry that gives an actual idea of what motivic integration is about, beyond it being an idea that Kontsevich had.)
added this sentences:
What is called motivic integration is an upgrade of p-adic integration to a geometric integration theory obtained by replacing the p-adic integers by a formal power series ring over the complex numbers.
p-adic integration is very cool indeed. I seem to remember it helping in counting subgroups of p-groups matching certain criteria. I also seem to remember the ideas lead to computations of invariants of certain moduli spaces that arise in representation theory. But it has been a few years since I looked at them. Glad to see the technique is getting wider use.
I took that sentence from the Introduction of the book. But by all means, somebody please expand on it.
Added a more detailed and updated description to the ##Idea section, while removing as little as possible of the existing content. Also added links to two highly relevant pages: arc space and Greenberg scheme.
Charlie Conneen
Rewrote idea section to one starting
Motivic integration_ attaches to certain subsets of arc schemes of varieties an element in a Grothendieck ring of varieties in a manner close in spirit to Euler characteristics. Technically it may be viewed as one of generalizations of p-adic integration
I think that p-adic integration is more technical and misterious to an outsider than the viewpoint of Euler characteristics as a version of integration.
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