Nebraska Cooperative Fish & Wildlife Research Unit


Date of this Version

Winter 2017


2017 Rocky Mountain Mathematics Consortium


JOURNAL OF COMMUTATIVE ALGEBRA Volume 9, Number 4, Winter 2017


Let (R,m,K) be a local ring, and let M be an R-module of finite length. We study asymptotic invariants, bfi (M,R), defined by twisting with Frobenius the free resolution of M. This family of invariants includes the Hilbert-Kunz multiplicity (eHK (m,R) = BF0 (K,R)). We discuss several properties of these numbers that resemble the behavior of the Hilbert-Kunz multiplicity. Furthermore, we study when the vanishing of BFI (M,R,) implies that M complete characterization of the vanishing of BFi (M,R0 for one-dimensional rings. As a consequence of our methods we give conditions for the non-existence of syzygies of finite length.