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Pré-Publication, Document De Travail Année : 2013

The convergence Newton polygon of a $p$-adic differential equation III : global decomposition and controlling graphs

Résumé

We deal with locally free $\mathcal{O}_X$-modules with connection over a Berkovich curve $X$. As a main result we prove local and global decomposition theorems of such objects by the radii of convergence of their solutions. We also derive a bound of the number of edges of the controlling graph, in terms of the geometry of the curve and the rank of the equation. As an application we provide a classification result of such equations over elliptic curves.

Dates et versions

hal-00871215 , version 1 (09-10-2013)

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Jérôme Poineau, Andrea Pulita. The convergence Newton polygon of a $p$-adic differential equation III : global decomposition and controlling graphs. 2013. ⟨hal-00871215⟩
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