论文标题
高几何积分模型$ P $和HASSE - WITT矩阵
Hypergeometric Integrals Modulo $p$ and Hasse--Witt Matrices
论文作者
论文摘要
当高几何解决方案是一维积分时，我们考虑$ \ Mathbb c $上的Kz微分方程。我们还考虑了有限字段$ \ mathbb f_p $上的相同的微分方程。我们研究了这些微分方程在$ \ Mathbb f_p $上的多项式解决方案的空间，该方程在V. Schechtman和第二作者的先前作品中构建。使用hasse-witt矩阵，我们将这些多项式解决方案在$ \ mathbb f_p $上识别出空间双重的空间，并在相关曲线上的某个常规差分子空间。我们还通过$ \ Mathbb f_p $与$ \ Mathbb C $上的超几何解决方案相关联的这些多项式解决方案。
We consider the KZ differential equations over $\mathbb C$ in the case, when the hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $\mathbb F_p$. We study the space of polynomial solutions of these differential equations over $\mathbb F_p$, constructed in a previous work by V. Schechtman and the second author. Using Hasse-Witt matrices we identify the space of these polynomial solutions over $\mathbb F_p$ with the space dual to a certain subspace of regular differentials on an associated curve. We also relate these polynomial solutions over $\mathbb F_p$ and the hypergeometric solutions over $\mathbb C$.
