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PD Operads and Explicit Partition Lie Algebras

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arxiv 2104.03870 v6 pith:5GYOSBDO submitted 2021-04-08 math.AG math.AT

Lukas Brantner , Ricardo Campos , Joost Nuiten This is my paper · ORCID
classification math.AGmath.AT
keywords algebrasoperadspartitioncasecharacteristicderiveddualityexplicit
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Infinitesimal deformations are governed by partition Lie algebras. In characteristic $0$, these higher categorical structures are modelled by differential graded Lie algebras, but in characteristic $p$, they are more subtle. We give explicit models for partition Lie algebras over general coherent rings, both in the setting of spectral and derived algebraic geometry. For the spectral case, we refine operadic Koszul duality to a functor from operads to divided power operads, by taking refined linear duals of $\Sigma_n$-representations. The derived case requires a further refinement of Koszul duality to a more genuine setting.

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Cited by 2 Pith papers

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  1. Modular fixed points in equivariant homotopy theory

    math.AT 2025-06 conditional novelty 8.0 of 10

    The derived ∞-category of permutation modules is equivalent to modules over the Eilenberg-MacLane spectrum of the constant Mackey functor, and the equivariant modular fixed point functor recovers Balmer-Gallauer's, gi...

  2. Theta-Categories and Tannakian duality

    math.AG 2025-08 conditional novelty 7.0 of 10

    Theta-categories are symmetric monoidal infinity-categories with an LSym monad, and every neutralized Tannakian Theta-category is equivalent to the ind-perfect complexes on its stack of LSym-fiber functors.

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