论文标题
对角F-Splitting和理想的象征力量
Diagonal F-splitting and Symbolic Powers of Ideals
论文作者
论文摘要
让$ j $是强烈的$ f $ f $ f $ f $ f $ -split ring $ r $在$ f $ finite字段上基本上是有限类型的理想选择。我们表明$ j^{s+t} \ subseteqτ（j^{s -ε}）τ（j^{t -ε}）$ for ALL $ S，T，T，ε> 0 $ for公式有意义。我们使用它来显示在这种情况下主要理想的符号和普通能力之间的许多新颖遏制，其中包括所有确定环和大量的带有积极特征的圆环环。特别是，我们表明$ p^{（2HN）} \ subseteq p^n $对于所有prime Ideals $ p $ a高$ h $在此类戒指中。
Let $J$ be any ideal in a strongly $F$-regular, diagonally $F$-split ring $R$ essentially of finite type over an $F$-finite field. We show that $J^{s+t} \subseteq τ(J^{s - ε}) τ(J^{t-ε})$ for all $s, t, ε> 0$ for which the formula makes sense. We use this to show a number of novel containments between symbolic and ordinary powers of prime ideals in this setting, which includes all determinantal rings and a large class of toric rings in positive characteristic. In particular, we show that $P^{(2hn)} \subseteq P^n$ for all prime ideals $P$ of height $h$ in such rings.
