- Acta Math.
- Volume 214, Number 2 (2015), 357-393.
The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves
We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic zero. Relying on work of the second author who investigated its properties on affinoid domains of the affine line, we prove that its slopes give rise to continuous functions that factorise by the retraction through a locally finite subgraph of the curve.
Acta Math. Volume 214, Number 2 (2015), 357-393.
Received: 3 June 2014
First available in Project Euclid: 30 January 2017
Permanent link to this document
Digital Object Identifier
Zentralblatt MATH identifier
Primary: 12H25: $p$-adic differential equations [See also 11S80, 14G20]
Secondary: 14G22: Rigid analytic geometry
2015 © Institut Mittag-Leffler
Poineau, Jérôme; Pulita, Andrea. The convergence Newton polygon of a p -adic differential equation II: Continuity and finiteness on Berkovich curves. Acta Math. 214 (2015), no. 2, 357--393. doi:10.1007/s11511-015-0127-8. https://projecteuclid.org/euclid.acta/1485802424