DMS Algebra Seminar

Speaker: Prashanth Sridhar, Auburn, 

Title: Periodicity of Fitting Ideals in Free Resolutions

Abstract: We examine the periodicity of ideals of minors in minimal free resolutions of finitely generated modules over local rings with a focus on their asymptotic behavior. The heuristics rely on the general principle that the initial part of the resolution is influenced by the module’s relations, while the singularities of the ring have a telling effect on the asymptotic behavior. For example, we show that for any finite module over a local complete intersection, the Fitting ideals of any size in its minimal free resolution are eventually 2-periodic (although the resolution is not). Moreover, if the stable value of a given size of minors is non-zero, it contains some power of the Jacobian ideal. Results of this type hold true in other settings as well (ex: Golod rings or residue field over any local ring), but do not hold in general.

This is joint work with Michael K. Brown and Hailong Dao.