Nebraska Cooperative Fish and Wildlife Research Unit
Date of this Version
Winter 2017
Citation
2017 Rocky Mountain Mathematics Consortium
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.
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Aquaculture and Fisheries Commons, Environmental Indicators and Impact Assessment Commons, Environmental Monitoring Commons, Natural Resource Economics Commons, Natural Resources and Conservation Commons, Water Resource Management Commons
Comments
JOURNAL OF COMMUTATIVE ALGEBRA Volume 9, Number 4, Winter 2017