Generalized hypergeometric arithmetic D-modules under a p-adic non-Liouvilleness condition

2019/01/11 by Miyatani, Kazuaki
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03488

Abstract

We prove that the arithmetic \mathscrD-modules associated with the p-adic generalized hypergeometric differential operators, under a p-adic non-Liouvilleness condition on parameters, are described as an iterative multiplicative convolution of (hypergeometric arithmetic) \mathscrD-modules of rank one. As a corollary, we prove the overholonomicity of hypergeometric arithmetic \mathscrD-modules under a p-adic non-Liouvilleness condition.

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