Multiplicity bounds in prime characteristic
arXiv:1804.11288
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.