Multiplicity bounds in prime characteristic

2018/04/30 by Mordechai Katzman, Katzman, Mordechai, Wenliang Zhang +1 · 1 citation
Mathematics · #13A35 #13H15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.11288

openalex publication_date 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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