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Apr 18, 2022 at 19:21 comment added Jon Pridham Brantner-Mathew isn't just char $p$. Section 6 does any complete local (simplicial or $E_{\infty}$) base, so includes zero and mixed characteristic. Section 5 of the same paper, and in particular Corollary 5.59, gives statements for other operads.
Apr 18, 2022 at 19:19 comment added Tim Campion @user40276 Thanks, this is super-helpful! It's also possible I've chosen the "wrong" precise technical statement of my question, on account of not knowing enough about the subject.
Apr 18, 2022 at 19:17 comment added user40276 If I've understood your question, Nuiten generalised Koszul duality for general base space (actually connective of characteristic $0$). See imag.umontpellier.fr/~nuiten/Writing/KoszulDualityLieAlgd.pdf . For characteristic $p$, there's Brantner-Mathew's arxiv.org/pdf/1904.07352.pdf .
Apr 18, 2022 at 18:24 history edited Tim Campion CC BY-SA 4.0
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Apr 18, 2022 at 18:17 history asked Tim Campion CC BY-SA 4.0