Dao–Takahashi's finite-radius conjecture for resolving subcategories

Let RR be a Cohen–Macaulay local ring. Let X\operatorname{\mathcal{X}} be a resolving subcategory of finitely generated RR-modules with finite radius. Dao–Takahashi's conjecture. Then X\operatorname{\mathcal{X}} is contained in the category CM(R)\operatorname{CM}(R) of maximal Cohen–Macaulay RR-modules. Dao and Takahashi proposed this conjecture in connection with the radius of resolving subcategories; it is known to hold when RR is a complete intersection, while the statement in general remains open.

Sources & referencesView supporting material

Primary source

Arash Sadeghi and Ryo Takahashi, “Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi”, arXiv:1710.10018 (2017).

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