Tuesday, February 27, 14:00, 7.527

Rudradip Biswas (Warwick), Applications of a new findim concept to derived categories arising in representation theory.

Abstract:
In a recent preprint [1], we introduced a definition of finitistic dimension for essentially small triangulated categories and showed that when this dimension is finite, the existence of a bounded t-structure implies that the category is invariant under completion, thereby generalizing some remarkable theorems of Neeman [3]. In this talk, I will focus on artin algebras and illustrate how this dimension behaves on the derived category of perfect complexes, the derived bounded category, and the singularity category. For artin algebras, under this treatment, we get many interesting new results and applications, including new proofs of older (obscure) facts. I will also show how our definition relates to Henning Krause's new definition of findim for triangulated categories [2].

References:
[1] R. Biswas, H. Chen, K. Manali Rahul, C. Parker, and J. Zheng. "Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories." arXiv:2401.00130
[2] H. Krause. "The finitistic dimension of a triangulated category." arXiv:2307.12671
[3] A. Neeman. "Bounded t-structures on the category of perfect complexes." Acta Math, to appear.