Upper bound of multiplicity in prime characteristic

2019/01/03 by Huong, Duong Thi, Quy, Pham Hung
#13A35 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.00849

Abstract

Let (R, \frak m) be a local ring of prime characteristic p of dimension d with the embedding dimension v. Suppose the Frobenius test exponent for parameter ideals Fte(R) of R is finite, and let Q = p^Fte(R). It is shown that e(R) ≤ Q^v-d \binomvd. We also improve our bound for F-nilpotent rings. Our result extends the main results of Huneke and Watanabe and of Katzman and Zhang.

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