2018/09/28 by Andrew R. Kustin, Kustin, Andrew R., Liana M. Şega +1
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1809.11094
We prove that every quasi-complete intersection ideal is obtained from a pair of nested complete intersection ideals by way of a flat base change. As a by-product we establish a rigidity statement for the minimal two-step Tate complex associated to an ideal I in a local ring R. Furthermore, we define a minimal two-step complete Tate complex T for each ideal I in a local ring R; and prove a rigidity result for it. The complex T is exact if and only if I is a quasi-complete intersection ideal; and in this case, T is the minimal complete resolution of R/I by free R-modules.