A Comparison Theorem for $p$-adic GKZ Hypergeometric $\mathcal{D}$-Modules and Complexes

We compare the $p$-adic GKZ hypergeometric complex with the hypergeometric arithmetic $\mathcal{D}$-module defined via six functors. Under the $p$-adic semi-nonresonance condition, the natural comparison morphism is a quasi-isomorphism. We prove concentration of the $p$-adic GKZ hypergeometric complex in degree $n$, establish overholonomicity under another non-Liouville hypothesis. When $(q-1)\gamma \in {\mathbb{Z}}^n$, we construct a Frobenius structure on its $n$-th cohomology and prove that its restriction to the nondegenerate locus is an overconvergent $F$-isocrystal of rank $n!\mathrm{vol}(\mathrm{\Delta })$.