p-adic hypergeometric \mathscrD^†(∞)-module and exponential sums on reductive groups

2025/12/12 by Li, Xuanyou, Liu, Chenhan
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.11302

Abstract

We study the p-adic analogue of the ℓ-adic hypergeometric sheaves for reductive groups, called the hypergeometric \mathscrD^†(∞)-modules. They are overholonomic objects in the derived category of arithmetic \mathscrD-modules with Frobenius structures. Over the non-degenerate locus, the hypergeometric \mathscrD^†(∞)-modules define F-isocrystals overconvergent along the complement of the non-degenerate locus. As an application, we use the theory of L-functions of overholonomic arithmetic \mathscrD-modules to study hypergeometric exponential sums on reductive groups.

Citations

• Hypergeometric \mathcal D-modules and exponential sums for reductive groups
• Equivariant D-modules

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