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Triangulated categories with a single compact generator and two Brown representability theorems

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arxiv 1804.02240 v5 pith:ATS3KXUO submitted 2018-04-06 math.CT

classification math.CT
keywords categoriesrepresentabilitytheoremstriangulatedapproximablebrowncompactdevelop
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We develop the general formalism of approximable triangulated categories, and prove two representability theorems.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Localizing invariants of inverse limits

    math.KT 2025-02 conditional novelty 8.0 of 10

    Continuous K-theory of nuclear modules on Spf(R^hat_I) is isomorphic to lim_n K(R/I^n), via internal projectivity and strongly Mittag-Leffler inverse sequences.

  2. Remarks on diagonal dimension for algebraic stacks

    math.AG 2026-05 unverdicted novelty 6.0 of 10

    For smooth, separated, quasi-DM stacks over a regular affine scheme, the diagonal dimension is bounded by a formula in dim R, dim U, and cd(Y); for varieties with mild singularities it is at most 2·dim X.

  3. Approximable Triangulated Categories and Reflexive DG-categories

    math.AG 2024-11 accept novelty 6.0 of 10

    A locally finite approximable DG-category with a strong generator inside its finitely valued modules is finite-reflexive; this yields reflexivity for proper schemes, Azumaya algebras, and proper connective DG-algebras.

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