Back to Commutative Algebra Seminar: Spring 2025
Commutative Algebra Seminar
Date: Friday, Mar 21, 2025
Time: 2:00PM - 3:00PM
Location: LCB 222
Janina Letz
Bielefeld
Title |
Generation time for tensor products and Koszul objects in triangulated categories |
Abstract |
The derived category of modules over a commutative ring captures many properties of the ring. One approach is to study its triangulated structure through finite building. An object $X$ finitely builds an object $Y$, if $Y$ can be obtained from $X$ by taking cones, suspensions and retracts. The $X$-level measures the number of cones required in this process. This recovers various classical invariants as projective dimension and Loewy length. I will explain the behavior of level with respect to tensor products in an enhanced triangulated category. I will further present applications to Koszul objects, which generalize Koszul complexes. This is joint work with Marc Stephan. |
Commutative Algebra