Back to Commutative Algebra Seminar: Spring 2024
Commutative Algebra Seminar
Date: Friday, Feb 2, 2024
Time: 2:30PM
Location: LCB 215
note unusual time
Souvik Dey
Charles University
Title |
Finitistic dimension and singularity categories |
Abstract |
Let A be a Noetherian ring (not necessarily commutative). When is there a uniform upper bound on the projective dimensions of all (left) A-modules of finite projective dimension? When A is commutative, it follows from the works of Bass and Gruson-Raynaud, that this is the case if and only if A has finite Krull dimension. The question of whether such a uniform upper bound exists for Artin algebras, even when restricted to finitely generated modules only, was first publicized by Bass in the 1960s. This question, since known as the finitistic dimension conjecture, remains open even after half a century. In this talk, based on ongoing joint work with Jan Stovicek, we will present some criteria for the existence of such uniform upper bounds in terms of certain form of generation in singularity categories. One ingredient of our approach is based on a generalization of the “delooping level” of Gélinas. |
Commutative Algebra