Ghosts and congruences for $p^s$-approximations of hypergeometric periods

Abstract

We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and KZ equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application we show that the simplest example of a $p$-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of the monodromy group.

Latex, 30 pages; v.2: misprints corrected, subsection 7.2 added, v.3: misprint in the title corrected, a reference updated