Nebraska Cooperative Fish and Wildlife Research Unit

 

Date of this Version

Winter 2017

Citation

2017 Rocky Mountain Mathematics Consortium

Comments

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

Abstract

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.

Share

COinS