Convergence polygons for connections on nonarchimedean curves

2015/05/07 by Kedlaya, Kiran S.
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1505.01890

Abstract

This is a survey article on ordinary differential equations over nonarchimedean fields based on the author's lecture at the 2015 Simons Symposium on nonarchimedean and tropical geometry. Topics include: the convergence polygon associated to a differential equation (or a connection on a curve); links to the formal classification of differential equations (Turrittin-Levelt); index formulas for de Rham cohomology of connections; ramification of finite morphisms; relations with the Oort lifting problem on automorphisms of curves. The appendices include some new technical results and an extensive thematic bibliography.

Related

• The convergence Newton polygon of a p-adic differential equation IV : controlling graphs
• The convergence Newton polygon of a p-adic differential equation III : global decompositions
• The convergence Newton polygon of a p-adic differential equation V : local index theorems
• Continuity of the radius of convergence of differential equations on\n p-adic analytic curves
• Applications of singular connections in symplectic and almost complex geometry