04/08/2025
The next Algebra Seminar will be Friday, April 11th at 2:15pm in Carnegie 219.
Speaker: Oana Veliche of Northeastern University
Title: On a construction of a minimal free resolutions of the residue field of a codepth 3 local ring
Abstract: In a paper with Van Nguyen we gave a description of a truncated minimal free resolution, up to homological degree five, of the residue field k over any local Noetherian ring (R,m,k) of any codepth. This description relies on the graded commutative algebra structure of the Koszul homology A=H(K), where K is the Koszul complex of the maximal ideal. The free resolution is given as building blocks in terms of the Koszul complex K. In a subsequent paper we constructed the entire free resolution of the residue field over a complete intersection ring, using an iterated mapping cone construction.
In my talk, I will discuss how the mapping cone construction in general can yield a minimal free resolution of k over other classes of rings. In particular, for local ring (R,m,k) of class T of codepth 3 (that is part of the Weyman and Avramov-Kustin-Miller classification), we construct a graded resolution of k over A and then from it we obtain the minimal free resolution of k over R.
Don't forget about our wonderful web site. https://www.joshpollitz.com/algebra-seminar.
