Multiplicity bounds in prime characteristic

Mordechai Katzman; Wenliang Zhang

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arXiv · 1804.11288

Multiplicity bounds in prime characteristic

Mordechai Katzman·Wenliang Zhang

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Abstract

We extend a result by Huneke and Watanabe bounding the multiplicity of $F$-pure local rings of prime characteristic in terms of their dimension and embedding dimensions to the case of $F$-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 $F$-injective type.

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Mordechai Katzman, Wenliang Zhang. 2018-04-30. Multiplicity bounds in prime characteristic. https://arxiv.org/abs/1804.11288

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