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arXiv · 2606.09398

Colocalizing subcategories on differentially graded algebras

Leovigildo Alonso·Ana Jeremías·Eduardo Loureiro
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Abstract

Let $A$ be a bounded non positive commutative differential graded algebra $A$. Let $\mathbf{D}(A)$ its derived category of DG-modules. If $\mathbf{D}(A)$ is generated by the DG-modules corresponding to the residue fields of the ordinary ring $H^0(A)$ then its localizing subcategories and its colocalizing subcategories are in bijection with the subsets of $\textrm{Spec}(H^0(A))$. These results generalize well-known theorems by A. Neeman (from 1992 and 2011, respectively), because any Noetherian ring satisfies this condition.

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Leovigildo Alonso, Ana Jeremías, Eduardo Loureiro. 2026-06-08. Colocalizing subcategories on differentially graded algebras. https://arxiv.org/abs/2606.09398

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