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arXiv · 2602.01761

Auslander correspondence for proper connective DG-algebras via extended module categories

Nao Mochizuki
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Abstract

We establish a $d$-dimensional Auslander correspondence for $d$-truncated proper connective DG-algebras via $d$-extended module categories. A $d$-truncated proper connective DG-algebra $\Gamma$ is called Auslander if its $d$-extended module category is a $d$-Auslander extriangulated category. Our main theorem gives a one-to-one correspondence: for any $d$-truncated proper connective DG-algebra $\Lambda$ whose $d$-extended module category has finitely many indecomposable objects, the DG-endomorphism algebra of an additive generator is Auslander, and conversely every Auslander $d$-truncated proper connective DG-algebra arises in this way.

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Nao Mochizuki. 2026-02-02. Auslander correspondence for proper connective DG-algebras via extended module categories. https://arxiv.org/abs/2602.01761

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