Nao Mochizuki

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math.RT2026

Extended Module Categories in Higher Cluster Tilting Theory

Nao Mochizuki

In this paper, we study ideal quotients of triangulated categories by higher cluster tilting subcategories. Koenig and Zhu proved that the ideal quotient by a $2$ -cluster tilting s…

math.RT2026

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

Nao Mochizuki

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-alg…

math.RT2025

On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras

Nao Mochizuki, Marvin Plogmann

We prove that, for a proper connective dg algebra $A$ with cohomology concentrated in degrees between $1 - d$ and $0$ , the extended heart $\mathcal{D}^{fd}(A)^{(-d,0]}\subseteq \math…