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Approximability and Rouquier dimension for noncommutative algebras over schemes

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arxiv 2408.04561 v3 pith:RUCQCDXK submitted 2024-08-08 math.AG math.ACmath.RA

Timothy De Deyn , Pat Lank , Kabeer Manali Rahul This is my paper · ORCID
classification math.AGmath.ACmath.RA
keywords algebrasdimensionalgebraapproximabilityneemannoetheriannoncommutativeopen
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This work is concerned with approximability (\`{a} la Neeman) and Rouquier dimension for triangulated categories associated to noncommutative algebras over schemes. Amongst other things, we establish that the category of perfect complexes of a Noetherian quasi-coherent algebra over a separated Noetherian scheme is strongly generated if, and only if, there exists an affine open cover where the algebra has finite global dimension. As a consequence, we solve an open problem posed by Neeman. Further, as a first application, we study the existence of generators for Azumaya algebras.

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Cited by 2 Pith papers

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  1. 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.

  2. Categorical absorption for hereditary orders

    math.AG 2025-05 conditional novelty 6.0 of 10

    A hereditary order on a curve is shown to admit a strong C-linear semiorthogonal decomposition obtained from the deformation absorption of singularities in its fiber over a ramified point.

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