Spectrum of p-adic linear differential equations I: the shape of the spectrum

• Tinhinane A. Azzouz ^[1]
  1. [1] Yau Mathematical Sciences Center, Tsinghua University, Beijing, China Beijing Institute of Mathematical Sciences and Applications, Beijing, China
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 1, 2024, págs. 2-66
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper extends our previous works Azzouz (Math Z 296(3–4): 1613–1644, 2020;

    Number Theory 231:139–157, 2022) on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with constant coefficients or over a field of formal power series. In this paper, we investigate the spectrum of p-adic differential equations at a generic point on a quasi-smooth curve. This analysis allows us to establish a significant connection between the spectrum and the spectral radii of convergence of a differential equation when considering the affine line. Furthermore, the spectrum offers a more detailed decomposition compared to Robba’s decomposition based on spectral radii Robba (Ann Math 101(2):280–316, 1975).