p-adic Generalized Hypergeometric Equations from the Viewpoint of Arithmetic D-modules
Abstract
We study the $p$-adic (generalized) hypergeometric equations by using the theory of multiplicative convolution of arithmetic $\mathscr{D}$-modules. As a result, we prove that the hypergeometric isocrystals with suitable rational parameters have a structure of overconvergent $F$-isocrystals.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2016
- DOI:
- 10.48550/arXiv.1607.04852
- arXiv:
- arXiv:1607.04852
- Bibcode:
- 2016arXiv160704852M
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory
- E-Print:
- 33 pages