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arXiv · 1505.01890

Convergence polygons for connections on nonarchimedean curves

Kiran S. Kedlaya
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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.

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Kiran S. Kedlaya. 2015-05-07. Convergence polygons for connections on nonarchimedean curves. https://arxiv.org/abs/1505.01890

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