Algebra Seminar - Vincent Gelinas
University of Toronto
Title: Constructing infinite free resolutions for rings of Krull dimension one via noncommutative Artinian rings
Abstract: The classical Hilbert Syzygy Theorem states that finitely generated modules over a polynomial ring Q = C[x_0, ..., x_n] have finite projective resolutions. The Auslander-Buchsbaum-Serre Theorem states that the same holds for Q/I if and only if Spec(Q/I) is smooth. When the latter is singular, one often seeks to understand the structure of modules with infinite minimal projective resolution, in particular their asymptotic behavior. When dim(Q/I) <=1, under modest technical assumptions and using recent results of Buchweitz-Iyama-Yamaura, we will show how to construct all tails of minimal projective resolutions over Q/I via an associated Artinian ring L which often leads to complete classifications or at least an understanding of their basic invariants.