Commutative Algebra Seminar

Let R be a regular local ring with residue field k and I a perfect ideal of R of grade 3. In 1978, Buchsbaum and Eisenbud showed that a minimal free resolution of R/I has a differential graded (DG) algebra structure, which induces a structure on the Tor algebra. By independent results of Weyman and of Avramov, Kustin, and Miller, this graded algebra structure may be classified into different classes. The classification is incomplete in the sense that it remains open which algebra structures actually occur; this realizability question was formally raised by Avramov in 2012. We survey which classes have been realized in the literature and detail the presenter's contributions to further answer the realizability question. Speaker(s): Alexis Hardesty (Texas Tech)