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nLab > Latest Changes: motivic integration

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 21st 2018

    added pointer to this new textbook

    • Antoine Chambert-Loir, Johannes Nicaise, JulienSebag, Motivic integration, Birkhaeuser 2018

    (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.)

    diff, v14, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 21st 2018

    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.

    diff, v14, current

    • CommentRowNumber3.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 21st 2018
    • (edited Sep 21st 2018)

    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.

    proof that I didn’t pull this out of my ass

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 22nd 2018

    Yes, we need some experts. I think the topic is broader than the first section suggests, e.g., to include integration over fields k((t))k((t)), kk of characteristic 00. But I don’t know what the full range might be.

    diff, v15, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2018

    I took that sentence from the Introduction of the book. But by all means, somebody please expand on it.

  6. add references to arc space and Greenberg scheme, schemes on which motivic integration is done.

    Charlie Conneen

    diff, v18, current

  7. 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

    diff, v19, current

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeJul 4th 2023

    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.

    https://people.math.harvard.edu/~mpopa/571/chapter6.pdf

    diff, v20, current

1 to 8 of 8

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