Local and global structure of connections on nonarchimedean curves

Abstract

Consider a vector bundle with connection on a p-adic analytic curve in the sense of Berkovich. We collect some improvements and refinements of recent results on the structure of such connections, and on the convergence of local horizontal sections. This builds on work from the author's 2010 book and on subsequent improvements by Baldassarri and Poineau-Pulita.

v3: 82 pages; refereed version

References in corpus (4)

• Relative p-adic Hodge theory: Foundations
• Cohomology of arithmetic families of (phi,Gamma)-modules
• Continuity of the radius of convergence of p-adic differential equations on Berkovich analytic spaces
• The convergence Newton polygon of a $p$-adic differential equation V : local index theorems

Cited by in corpus (6)

• Etale and crystalline companions, I
• The convergence Newton polygon of a $p$-adic differential equation V : local index theorems
• Spectrum of a linear differential equation over a field of formal power series
• Optimal bases for direct images of $p$-adic differential modules over discs
• Variation of the Swan conductor of an ${\mathbb{F}}_{\ell }$-sheaf on a rigid disc
• Pushforwards of $p$-adic differential equations