arXiv subjects

Charley Cummings

Publications and source records attributed to Charley Cummings.

5 recordsLinked to original sources

arXiv2026

Codistinguished abelian subcategories

We introduce codistinguished abelian subcategories of triangulated categories, which generalise Jorgensen's proper abelian subcategories and are dual to Linckelmann's distinguished abelian subcategories. We show that they come equipped with a non-trivial exact structure induced by the ambient triangulated category, and that every exact structure on an abelian category arises in this way. We also show that fully faithful adjunction triples produce new codistinguished abelian subcategories from old.

math.RT↗

arXiv2025

An equivalence linking CM-types $A_\infty$ and $D_\infty$

We show that, for a specific grading, the stable categories of graded maximal Cohen-Macaulay modules over hypersurfaces of type $A_\infty$ and $D_\infty$ are equivalent.

math.RT↗

arXiv2024

Metric completions of discrete cluster categories

Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a coaisle metric this yields a new triangulated category which can be interpreted as a topological completion of the associated combinatorial model. Moreover, we show that the completion of any triangulated category with respect to an internal aisle metric is a thick subcategory of the triangulated category itself.

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arXiv2022

Left-right symmetry of finite finitistic dimension

We show that the finitistic dimension conjecture holds for all finite dimensional algebras if and only if, for all finite dimensional algebras, the finitistic dimension of an algebra being finite implies that the finitistic dimension of its opposite algebra is also finite. We also prove the equivalent statement for injective generation.

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arXiv2020

Ring Constructions and Generation of the Unbounded Derived Module Category

We consider the smallest triangulated subcategory of the unbounded derived module category of a ring that contains the injective modules and is closed under set indexed coproducts. If this subcategory is the entire derived category, then we say that injectives generate for the ring. In particular, we ask whether, if injectives generate for a collection of rings, do injectives generate for related ring constructions and vice versa. We provide sufficient conditions for this statement to hold for various constructions including recollements, ring extensions and module category equivalences.

math.RT↗