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arXiv · 1901.00849

Upper bound of multiplicity in prime characteristic

Duong Thi Huong·Pham Hung Quy
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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 $$e(R) \le Q^{v-d} \binom{v}{d}.$$ 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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Duong Thi Huong, Pham Hung Quy. 2019-01-03. Upper bound of multiplicity in prime characteristic. https://arxiv.org/abs/1901.00849

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