Prolongation of regular-singular connections on punctured affine line over a Henselian ring

Abstract

We generalize Deligne’s equivalence between the categories of regular-singular connections on the formal punctured disk and on the punctured affine line to the case where the base is a strictly Henselian discrete valuation ring of equal characteristic 0. We also provide a weaker result when the base is higher dimensional.

Keywords:

• Deligne’s equivalence
• Henselian discrete valuation ring
• regular-singular connection

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 12H05
• 13N15
• 18M05

Acknowledgments

We would like to thank the anonymous referee for his/her careful reading, pointing out a mistake in a previous version, and constructive suggestions leading to a significant improvement of our work.

Additional information

Funding

The research of Phùng Hô Hai and Phạm Thanh Tâm is funded by the International Center for Research and Postgraduate Training in Mathematics (Institute of Mathematics, VAST, Vietnam) under grant number ICRTM01_2020.06 and funded by Vingroup Joint Stock Company and supported by Vingroup Innovation Foundation (VinIF) under the project code VINIF.2021.DA00030. A part of this work has been carried out during Phùng Hô Hai’s visit at the Vietnam Institute of Advanced Study in Mathematics, he thanks the institute for its hospitality and financial support. The research of Đào Văn Thịnh was supported by the Postdoctoral program of Vietnam Institute for Advanced Study in Mathematics.