Gauss--Manin connections extend to holonomic coadmissible D-cap-modules

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.