标题： $p$-规范坐标的整体性 显示英文标题

标题： $p$-Integrality of canonical coordinates

摘要： 设$L$是一个系数在$\mathbb{Q}(z)$中的微分算子，其阶数为$n\geq2$，在零点处具有极大单峰单值群。 在本文中，我们感兴趣的是确定$L$的规范坐标是否属于$\mathbb{Z}_p[[z]]$。 为此，受P. Candelas、X. de la Ossa和D. van Straten~\cite{CD}的一个最近猜想的启发，我们研究当$L$具有一个强Frobenius结构$\Phi=(\phi_{i,j})_{1\leq i,j\leq n}\in M_n(\mathbb{Z}_p[[z]])$，使得$\phi_{1,1}(0)=1$的情况。然后，我们给出当$L$具有这样的强Frobenius结构时，$L$的规范坐标属于$\mathbb{Z}_p[[z]]$的充分必要条件。 显示英文摘要

摘要： Let $L$ be a differential operator with coefficients in $\mathbb{Q}(z)$ of order $n\geq2$ with maximal unipotent monodromy at zero. In this paper we are interested in determining when the canonical coordinate of $L$ belongs to $\mathbb{Z}_p[[z]]$. For this purpose, motivated by a recent conjecture due to P. Candelas, X. de la Ossa and D. van Straten~\cite{CD}, we study the situation when $L$ has a strong Frobenius structure $\Phi=(\phi_{i,j})_{1\leq i,j\leq n}\in M_n(\mathbb{Z}_p[[z]])$ such that $\phi_{1,1}(0)=1$. We then give a necessary and sufficient condition for the canonical coordinate of $L$ to belong to $\mathbb{Z}_p[[z]]$ when $L$ has such a strong Frobenius structure.