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

Source abstract

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 $(q-1)γ\in\mathbb Z^n$, 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 $n!\operatorname{vol}(Δ)$.