论文标题
卷= $ p $ f $ for $ p $ for的理想的多样性公式
A Volume = Multiplicity formula for $p$-families of ideals
论文作者
论文摘要
在本文中，我们与某些理想家庭合作，称为$ p $ - 富裕的主要特征环。这个理想的家族存在于紧密封闭，希尔伯特·昆兹多重性和$ f $ signature的理论中。对于每个理想的$ p $ - 家族，我们都会附上一个称为$ p $ body的欧几里得对象，该物体类似于牛顿Okounkov的身体，与分级的理想家族相关。使用Hilbert-Kunz多重性的$ p $ bodies和代数属性的组合属性，我们在本文中建立了$ p $ -families的$ \ mathfrak {m} _ {m} _ {r} _ {r} $的多重公式 - 在Noyether localian local Ring Ring $ r $中的主要理想。
In this paper, we work with certain families of ideals called $p$-families in rings of prime characteristic. This family of ideals is present in the theories of tight closure, Hilbert-Kunz multiplicity, and $F$-signature. For each $p$-family of ideals, we attach a Euclidean object called $p$-body, which is analogous to the Newton Okounkov body associated with a graded family of ideals. Using the combinatorial properties of $p$-bodies and algebraic properties of the Hilbert-Kunz multiplicity, we establish in this paper a Volume = Multiplicity formula for $p$-families of $\mathfrak{m}_{R}$-primary ideals in a Noetherian local ring $R$.
