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

Abstract

We show that the $p$-adic KZ connection associated with the family of curves $y^q=(t-z_1)\cdots (t-z_{qg+1})$ 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.