In the 1960’s, Grothendieck showed that a commutative noetherian ring which admits a dualizing complex has finite Krull dimension. In 2018, Rickard showed that a finite-dimensional algebra A for which the localizing subcategory generated by the injective modules is equal to D(A) satisfies the finitistic dimension conjecture.
In this talk we explain how to view both of these results as special cases of a single result which is valid for any noncommutative noetherian ring which admits a dualizing complex.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
