标题： 关于空间$L_{m+1,n}$的算术和几何学 显示英文标题

标题： On the arithmetic and geometry of spaces $L_{m+1,n}$

摘要： 本文中，我们证明了关于特征为$p$的某些称为\emph{空间 $L_{m+1,n}$}的对数微分形式的$\mathbb{F}_p$-向量空间的若干新结果。 拓展前两位作者的先前工作，我们在许多情形下证明了关于空间$L_{m+1,n}$存在性的正面和负面结果，还对所有特征为$p=3$的空间$L_{12,2}$和$L_{15,2}$进行了分类。 所使用的创新工具包括 Moore 显示英文摘要

摘要： In this paper, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms in characteristic $p$ called \emph{spaces $L_{m+1,n}$}. Expanding the previous work by the first two authors, we prove positive and negative results for the existence of spaces $L_{m+1,n}$ in many situations, as well as a classification of all spaces $L_{12,2}$ and $L_{15,2}$ for $p=3$. The novel tools used are Moore determinants and computational algebra.