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A Comparison Theorem for p-adic GKZ Hypergeometric π’Ÿ-Modules and Complexes

  • Chenhan Liu
  • Hao Zhang
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Abstract

We compare the p-adic GKZ hypergeometric complex with the hypergeometric arithmetic π’Ÿ-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 (qβˆ’1)Ξ³βˆˆβ„€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!vol(Ξ”).

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Cite

BibTeXRIS
BibTeX
@misc{liu2026comparison,
  title = {{A Comparison Theorem for $p$-adic GKZ Hypergeometric $\mathcal D$-Modules and Complexes}},
  author = {Chenhan Liu and Hao Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12918},
  eprint = {2610.12918},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12918},
}
RIS
TY  - UNPB
TI  - A Comparison Theorem for p-adic GKZ Hypergeometric π’Ÿ-Modules and Complexes
AU  - Chenhan Liu
AU  - Hao Zhang
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12918
UR  - https://arxiv.org/abs/2610.12918
AB  - We compare the p-adic GKZ hypergeometric complex with the hypergeometric arithmetic π’Ÿ-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 (qβˆ’1)Ξ³βˆˆβ„€^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!vol(Ξ”).
ER  -