标题： Dwork型同余和$p$-进KZ连接 显示英文标题

标题： Dwork-type congruences and $p$-adic KZ connection

摘要： 我们证明与曲线族$y^q=(t-z_1)\dots (t-z_{qg+1})$相关的$p$-adic KZ联络有一个秩为$g$的不变子丛，而相应的复数KZ联络由于其单色表示的不可约性而没有非平凡的真子丛。 该不变子丛的构造基于相关Hasse--Witt矩阵的新Dwork型同余式。 显示英文摘要

摘要： We show that the $p$-adic KZ connection associated with the family of curves $y^q=(t-z_1)\dots (t-z_{qg+1})$ has an invariant subbundle of rank $g$, while the corresponding complex KZ connection has no nontrivial proper subbundles due to the irreducibility of its monodromy representation. The construction of the invariant subbundle is based on new Dwork--type congruences for associated Hasse--Witt matrices.