Year: 2026
Type: preprint
Abstract: We prove that the pushforwards of Gauss--Manin connections on smooth rigid analytic varieties along Zariski-open immersions are coadmissible and holonomic over Ardakov--Wadsley's sheaf D-cap of infinite order differential operators. This may be viewed as a rigid analytic variant of the classical theorem of Griffiths, Deligne, and Katz that Gauss-Manin systems have regular singularities after compactification. The proof combines p-adic de Rham comparison and Diao--Lan--Liu--Zhu's logarithmic Riemann--Hilbert correspondence with extendability results for log-connections with nilpotent residues. In the algebraic snc case, we also establish weak holonomicity via a p-adic Bernstein-Sato criterion of Bitoun and the first author.
Source: arXiv (Cornell University)
Authors: Bode, Andreas, Wiersig, Finn
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214713556