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nLab > Latest Changes: motivic Galois group

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2013

    stated a kind of Idea/definiton at motivic Galois group.

    Experts and experts-to-be, please check!

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJun 9th 2013
    • (edited Jun 9th 2013)
    • Annette Huber, Stefan Müller-Stach, On the relation between Nori motives and Kontsevich periods, arxiv/1105.0865

    We show that the spectrum of Kontsevich’s algebra of formal periods is a torsor under the motivic Galois group for mixed motives over the rational numbers. This assertion is stated without proof by Kontsevich and originally due to Nori. In a series of appendices, we also provide the necessary details on Nori’s category of motives.

    Note that this is involving the variant of the motivic Galois group for mixed motives. The entry had only the case of pure motives (The idea s the same, I see no reason for the restriction stated in the entry, so I put the remark there.)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2013

    Thanks! That’s very useful. I’ll have a look at the article

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 19th 2013

    I have briefly added a minimum cross-link between motivic Galois group and Grothendieck-Teichmüller group and a pointer to Drinfeld’s statement of the conjecture that the latter is a quotient of the former.

    More to be done here, but no time.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeAug 26th 2013

    I think that this conjecture is essentially already in the Esquisse of Grothendieck, isn’t it ? Of course, the Drinfeld contribution toward the rigorous theory is seminal here.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 26th 2013
    • (edited Aug 26th 2013)

    I don’t know much about the history of the conjecture. All I saw and heard was it being attributed to Drinfeld. But if you have more details, please add them to the entry!

    • CommentRowNumber7.
    • CommentAuthorJohn Baez
    • CommentTimeApr 14th 2023

    Pointed out that we tweak the category of pure numerical motives only by changing the braiding, or symmetry. (I said “symmetry”, but I find this word ambiguous sometimes.)

    diff, v19, current

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