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榎本 悠久氏（名古屋大学多元数理研究科）
Auslander-type correspondences for exact categories and cotilting modules
In this talk, I will give an Auslander-type correspondence for cotilting modules $U$ such that their Ext-perpendicular category $^¥perp U$ have finitely many indecomposables. The typical examples of such categories $^¥perp U$ are the category of Cohen-Macaulay modules over Iwanaga-Gorenstein algebras (and complete Cohen-Macaulay local ring), thus we can obtain a kind of classification of CM-finite algebras. Firstly, I will explain the Morita-type characterization of $^¥perp U$ as an exact category. Then, I will talk about an Auslander-type correspondence for exact categories, more precisely, a classification of exact structures on a given category using its Auslander algebra. Finally, by combining these results, we will obtain the correspondence for $^¥perp U$.