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nLab > Latest Changes: formal moduli problem

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2013
    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 17th 2019

    Added

    Lukas Brantner, Akhil Mathew, Deformation Theory and Partition Lie Algebras, arXiv:1904.07352

    diff, v12, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeNov 5th 2019
    There's a problem in Definition 1.1.

    FMPs are not required to preserve all pull-backs between small objects, but onty pull-backs along small morphisms.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 6th 2019

    Thanks for the alert.

    I have briefly added the missing clause now.

    But the entry remains a stub, waiting for somebody to expand on it.

    diff, v14, current

  5. Adds a brief elaboration on interpreting the infinitesmally-cartesian condition in obstruction theory.

    Jake Bian

    diff, v15, current

    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeJun 22nd 2022
    Would it make sense to add some comments about extensions of the FMP <-> Lie-alg equivalence?
    For instance:
    - there is Benjamin Hennion's work that extend the Pridham-Lurie theorem over a cdga (rather than just a field).
    - there is Joost Nuiten's work on the equivalence between Lie algebroids and formal thickenings of a derived affine scheme (this encompasses Hennion's work mentioned above).
    - there is Lurie's work (already in DAG X) about E_n-FMPs.
    - there is my work with Campos and Nuiten that generalizes the equivalence to the case of a pair of Koszul dual operads (the theorem of Lurie and Pridham corresponds to the (Com,Lie) duality).

    Finally, there is a nice reference on FMP, that is Toën's Bourbaki seminar: https://hal.archives-ouvertes.fr/hal-01253022v2

    Damien (Calaque)
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2022

    Would it make sense

    Certainly!

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTime1 day ago
    • (edited 1 day ago)

    added pointer to

    • Brice Le Grignou, Victor Roca i Lucio: A new approach to formal moduli problems [arXiv:2306.07227]

    (advertized this morning in Srni, by Bruno Vallette, as more explicit re-proof of the equivalence between formal moduli problems and dg-Lie algebras)

    diff, v20, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTime1 day ago

    and to

    • Arjen Baarsma: Deformation problems and L ∞L_\infty-algebras of Fréchet type, PhD thesis, Utrecht University (2019) [dspace:1874/386311, pdf]

    (advertised after Bruno’s talk by Gil Cavalcanti)

    diff, v20, current

1 to 9 of 9

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