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arXiv · 2408.04561

Approximability and Rouquier dimension for noncommutative algebras over schemes

Timothy De Deyn·Pat Lank·Kabeer Manali Rahul
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Abstract

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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Timothy De Deyn, Pat Lank, Kabeer Manali Rahul. 2024-08-08. Approximability and Rouquier dimension for noncommutative algebras over schemes. https://arxiv.org/abs/2408.04561

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