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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.
Related
BibTeX
@misc{bode2026gaussmanin,
title = {{Gauss--Manin connections extend to holonomic coadmissible D-cap-modules}},
author = {Andreas Bode and Finn Wiersig},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34312},
eprint = {2609.34312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34312},
}
RIS
TY - UNPB
TI - Gauss--Manin connections extend to holonomic coadmissible D-cap-modules
AU - Andreas Bode
AU - Finn Wiersig
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34312
UR - https://arxiv.org/abs/2609.34312
AB - 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.
ER -