Back to Commutative Algebra Seminar: Fall 2014
Commutative Algebra Seminar
Date: Friday, Sep 26, 2014
Time: 3:10PM - 4:00PM
Location: LCB 323
Jesse Burke
UCLA
Title |
Higher homotopies and Golod rings |
Abstract |
We study free resolutions of R = Q/I modules using A-infinity structures on Q-free resolutions. These higher homotopies give a very general change of rings theorem for free resolutions, and a construction of Q-free resolutions of all R-syzygies of R-modules. We use these tools to study Golod modules. The higher homotopies shed light on some old results, and give two new results: if the usual power series bound defining a Golod module is an equality in the first dim Q degrees, it is an equality in all degrees; and a construction of the minimal free resolution of every module over a Golod ring. |
Commutative Algebra