Dwork-type congruences and \(p\)-adic KZ connection (Q6191246)

Summary: 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. For the entire collection see [Zbl 1519.57002].