Multiplicity bounds in prime characteristic
Commutative Algebra
2018-08-14 v2
Abstract
We extend a result by Huneke and Watanabe bounding the multiplicity of -pure local rings of prime characteristic in terms of their dimension and embedding dimensions to the case of -injective, generalized Cohen-Macaulay rings. We then produce an upper bound for the multiplicity of any local Cohen-Macaulay ring of prime characteritic in terms of their dimensions, embedding dimensions and HSL numbers. Finally, we extend the upper bounds for the multiplicity of generalized Cohen-Macaulay rings in characteristic zero which have dense -injective type.
Cite
@article{arxiv.1804.11288,
title = {Multiplicity bounds in prime characteristic},
author = {Mordechai Katzman and Wenliang Zhang},
journal= {arXiv preprint arXiv:1804.11288},
year = {2018}
}