The Dwork-congruence criterion for divisible Hodge F-crystals

Let ${\cal P}$ be a CY(4)-operator with normalized holomorphic solution

$$f_0(z)=\sum_{n=0}^{\infty}c_nz^n,$$

and let ${\cal Q}$ be the associated CY(5)-operator with normalized holomorphic solution

$$F_0(z)=\sum_{n=0}^{\infty}d_nz^n.$$

The Dwork congruences are the congruences for the coefficients of these power series used in the source. The Dwork-congruence criterion. If the coefficients $c_n$ satisfy the Dwork congruences, then $H$ satisfies the conditions of Theorem when $g(z):=f^{(p-1)}_0(z)$; and if the coefficients $d_n$ satisfy the Dwork congruences, then the sub-$F$-crystal $G\subset\wedge^2H$ satisfies those conditions when $g(z):=F^{(p-1)}_0(z)$. This gives the polynomial choices used to obtain the divisible Hodge $F$-crystals in the source.