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Here, $\\mathrm{Frob}(-,-)$ denotes the $\\infty$-category of generalized Frobenius modules\n  as introduced in arXiv:2410.17102.\n  This generalizes our result from arXiv:2410.17102,\n  where we proved the above for regular Noetherian $\\mathbb{F}_p$-schemes.\n  As a byproduct we prove that the 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derived $\\infty$-category of Frobenius modules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Klaus Mattis, Timo Wei{\\ss}","submitted_at":"2025-10-27T12:27:20Z","abstract_excerpt":"We prove that for $X$ a quasi-compact $\\mathbb{F}_p$-scheme with affine diagonal (e.g.\\ $X$ quasi-compact\n  and separated) there is a t-exact equivalence\n  $\\mathcal D(\\mathrm{Frob}(\\mathrm{QCoh}(X),F_*)) \\to \\mathrm{Frob}(\\mathcal D(\\mathrm{QCoh}(X)),\\mathcal D(F_*))$\n  of stable $\\infty$-categories.\n  Here, $\\mathrm{Frob}(-,-)$ denotes the $\\infty$-category of generalized Frobenius modules\n  as introduced in arXiv:2410.17102.\n  This generalizes our result from arXiv:2410.17102,\n  where we proved the above for regular Noetherian $\\mathbb{F}_p$-schemes.\n  As a byproduct we prove that the 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