Journal of the London Mathematical Society· 2026Q1
Spectrum of p‐adic linear differential equations II: Variation of the spectrum
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- Q1SCImago
- 2026year
Short summary
The spectrum of p-adic linear differential equations is shown to be continuous on the skeleton of annuli and influenced by the controlling graph of radii of convergence.
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Key points
- The spectrum of p-adic linear differential equations is continuous on the skeleton of annuli.
- The spectrum is influenced by the controlling graph of radii of convergence.
- Approximating the connection enables accurate estimation of spectral radii of convergence.
- A refined decomposition theorem is presented and extended to neighborhoods of specific points.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract This paper explores the spectrum of ‐adic linear differential equations, extending previous findings to quasi‐smooth Berkovich curves. It focuses on the relationship between the spectrum and the radii of convergence by investigating the continuity and variation of the spectrum for these equations. The study reveals that the spectrum can be influenced by the controlling graph of the radii of convergence and is continuous on the skeleton of annuli. Furthermore, the paper demonstrates that approximating the connection allows for an accurate estimation of spectral radii of convergence. Key results include a refined decomposition theorem with respect to the spectrum and its extension to neighborhoods of specific points. The work builds upon earlier research and introduces new approaches for understanding the spectral properties of differential equations defined over quasi‐smooth curves.
The authors' abstract, as published at the source. Journal of the London Mathematical Society, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics